How to find a complex fraction - PSAT Math

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Question

Simplify:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

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Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{1 \cdot x}{x}$ - $\frac{2}{x}$}{$\frac{1 \cdot $x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x}{x}$ - $$\frac{2}{x}$}{$\frac{x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x-2}{x}$ $}{$\frac{x^{2}$$$+2}{x^{2}$} }$

$= $\frac{ x-2}{x}$ \div $$\frac{x^{2}$$$+2}{x^{2}$}$

$= $\frac{ x-2}{x}$ \cdot $$\frac{x^{2}$$$}{x^{2}$+2}$

$= $\frac{ x-2}{1}$ \cdot $\frac{x $}{x^{2}$$+2}$

$= $\frac{ $x^{2}$$-2x}{ $x^{2}$+2}$

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Question

Evaluate:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

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Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

$=\frac{ \frac{12}{4}$+\frac{1}{4}$}{$\frac{12}{4}$-$\frac{1}{4}$}$

$=\frac{ \frac{13}{4}$}{$\frac{11}{4}$ }$

$= $\frac{13}{4}$\div $\frac{11}{4}$$

$= $\frac{13}{4}$\cdot $\frac{4}{11}$$

$= $\frac{13}{1}$\cdot $\frac{1}{11}$$

$= $\frac{13}{11}$$

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Question

Simplify:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

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Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{1 \cdot x}{x}$ - $\frac{2}{x}$}{$\frac{1 \cdot $x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x}{x}$ - $$\frac{2}{x}$}{$\frac{x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x-2}{x}$ $}{$\frac{x^{2}$$$+2}{x^{2}$} }$

$= $\frac{ x-2}{x}$ \div $$\frac{x^{2}$$$+2}{x^{2}$}$

$= $\frac{ x-2}{x}$ \cdot $$\frac{x^{2}$$$}{x^{2}$+2}$

$= $\frac{ x-2}{1}$ \cdot $\frac{x $}{x^{2}$$+2}$

$= $\frac{ $x^{2}$$-2x}{ $x^{2}$+2}$

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Question

Evaluate:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

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Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

$=\frac{ \frac{12}{4}$+\frac{1}{4}$}{$\frac{12}{4}$-$\frac{1}{4}$}$

$=\frac{ \frac{13}{4}$}{$\frac{11}{4}$ }$

$= $\frac{13}{4}$\div $\frac{11}{4}$$

$= $\frac{13}{4}$\cdot $\frac{4}{11}$$

$= $\frac{13}{1}$\cdot $\frac{1}{11}$$

$= $\frac{13}{11}$$

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Question

Simplify:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

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Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{1 \cdot x}{x}$ - $\frac{2}{x}$}{$\frac{1 \cdot $x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x}{x}$ - $$\frac{2}{x}$}{$\frac{x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x-2}{x}$ $}{$\frac{x^{2}$$$+2}{x^{2}$} }$

$= $\frac{ x-2}{x}$ \div $$\frac{x^{2}$$$+2}{x^{2}$}$

$= $\frac{ x-2}{x}$ \cdot $$\frac{x^{2}$$$}{x^{2}$+2}$

$= $\frac{ x-2}{1}$ \cdot $\frac{x $}{x^{2}$$+2}$

$= $\frac{ $x^{2}$$-2x}{ $x^{2}$+2}$

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Question

Evaluate:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

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Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

$=\frac{ \frac{12}{4}$+\frac{1}{4}$}{$\frac{12}{4}$-$\frac{1}{4}$}$

$=\frac{ \frac{13}{4}$}{$\frac{11}{4}$ }$

$= $\frac{13}{4}$\div $\frac{11}{4}$$

$= $\frac{13}{4}$\cdot $\frac{4}{11}$$

$= $\frac{13}{1}$\cdot $\frac{1}{11}$$

$= $\frac{13}{11}$$

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Question

Simplify:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

Tap to reveal answer

Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{1 \cdot x}{x}$ - $\frac{2}{x}$}{$\frac{1 \cdot $x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x}{x}$ - $$\frac{2}{x}$}{$\frac{x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x-2}{x}$ $}{$\frac{x^{2}$$$+2}{x^{2}$} }$

$= $\frac{ x-2}{x}$ \div $$\frac{x^{2}$$$+2}{x^{2}$}$

$= $\frac{ x-2}{x}$ \cdot $$\frac{x^{2}$$$}{x^{2}$+2}$

$= $\frac{ x-2}{1}$ \cdot $\frac{x $}{x^{2}$$+2}$

$= $\frac{ $x^{2}$$-2x}{ $x^{2}$+2}$

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Question

Evaluate:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

Tap to reveal answer

Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

$=\frac{ \frac{12}{4}$+\frac{1}{4}$}{$\frac{12}{4}$-$\frac{1}{4}$}$

$=\frac{ \frac{13}{4}$}{$\frac{11}{4}$ }$

$= $\frac{13}{4}$\div $\frac{11}{4}$$

$= $\frac{13}{4}$\cdot $\frac{4}{11}$$

$= $\frac{13}{1}$\cdot $\frac{1}{11}$$

$= $\frac{13}{11}$$

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Question

Simplify:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

Tap to reveal answer

Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{1 \cdot x}{x}$ - $\frac{2}{x}$}{$\frac{1 \cdot $x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x}{x}$ - $$\frac{2}{x}$}{$\frac{x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x-2}{x}$ $}{$\frac{x^{2}$$$+2}{x^{2}$} }$

$= $\frac{ x-2}{x}$ \div $$\frac{x^{2}$$$+2}{x^{2}$}$

$= $\frac{ x-2}{x}$ \cdot $$\frac{x^{2}$$$}{x^{2}$+2}$

$= $\frac{ x-2}{1}$ \cdot $\frac{x $}{x^{2}$$+2}$

$= $\frac{ $x^{2}$$-2x}{ $x^{2}$+2}$

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Question

Evaluate:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

Tap to reveal answer

Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

$=\frac{ \frac{12}{4}$+\frac{1}{4}$}{$\frac{12}{4}$-$\frac{1}{4}$}$

$=\frac{ \frac{13}{4}$}{$\frac{11}{4}$ }$

$= $\frac{13}{4}$\div $\frac{11}{4}$$

$= $\frac{13}{4}$\cdot $\frac{4}{11}$$

$= $\frac{13}{1}$\cdot $\frac{1}{11}$$

$= $\frac{13}{11}$$

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Question

Simplify:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

Tap to reveal answer

Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{1 \cdot x}{x}$ - $\frac{2}{x}$}{$\frac{1 \cdot $x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x}{x}$ - $$\frac{2}{x}$}{$\frac{x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x-2}{x}$ $}{$\frac{x^{2}$$$+2}{x^{2}$} }$

$= $\frac{ x-2}{x}$ \div $$\frac{x^{2}$$$+2}{x^{2}$}$

$= $\frac{ x-2}{x}$ \cdot $$\frac{x^{2}$$$}{x^{2}$+2}$

$= $\frac{ x-2}{1}$ \cdot $\frac{x $}{x^{2}$$+2}$

$= $\frac{ $x^{2}$$-2x}{ $x^{2}$+2}$

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Question

Evaluate:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

Tap to reveal answer

Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

$=\frac{ \frac{12}{4}$+\frac{1}{4}$}{$\frac{12}{4}$-$\frac{1}{4}$}$

$=\frac{ \frac{13}{4}$}{$\frac{11}{4}$ }$

$= $\frac{13}{4}$\div $\frac{11}{4}$$

$= $\frac{13}{4}$\cdot $\frac{4}{11}$$

$= $\frac{13}{1}$\cdot $\frac{1}{11}$$

$= $\frac{13}{11}$$

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Question

Simplify:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

Tap to reveal answer

Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{1- \frac{2}{x}$}{1+ $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{1 \cdot x}{x}$ - $\frac{2}{x}$}{$\frac{1 \cdot $x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x}{x}$ - $$\frac{2}{x}$}{$\frac{x^{2}$$$}{x^{2}$} + $$\frac{2}{x^{2}$$}}$

$=\frac{\frac{ x-2}{x}$ $}{$\frac{x^{2}$$$+2}{x^{2}$} }$

$= $\frac{ x-2}{x}$ \div $$\frac{x^{2}$$$+2}{x^{2}$}$

$= $\frac{ x-2}{x}$ \cdot $$\frac{x^{2}$$$}{x^{2}$+2}$

$= $\frac{ x-2}{1}$ \cdot $\frac{x $}{x^{2}$$+2}$

$= $\frac{ $x^{2}$$-2x}{ $x^{2}$+2}$

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Question

Evaluate:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

Tap to reveal answer

Answer

Simplify the numerator and the denominator, then divide, as follows:

$$\frac{3+\frac{1}{4}$}{3-$\frac{1}{4}$}$

$=\frac{ \frac{12}{4}$+\frac{1}{4}$}{$\frac{12}{4}$-$\frac{1}{4}$}$

$=\frac{ \frac{13}{4}$}{$\frac{11}{4}$ }$

$= $\frac{13}{4}$\div $\frac{11}{4}$$

$= $\frac{13}{4}$\cdot $\frac{4}{11}$$

$= $\frac{13}{1}$\cdot $\frac{1}{11}$$

$= $\frac{13}{11}$$

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