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Common Core: High School - Algebra : Rational Expressions: CCSS.Math.Content.HSA-APR.D.7

Study concepts, example questions & explanations for Common Core: High School - Algebra

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All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #331 : Arithmetic With Polynomials & Rational Expressions

Simplify:

$\frac{x - 19}{x - 16} + \frac{x + 1}{x - 5}$

Possible Answers:

$\frac{2 x + 20}{2 x - 21}$

$\frac{ 2 x^{2} - 6 x + 79 }{ x^{2} - 21 x + 80 }$

$\frac{ 2 x^{2} - 39 x + 79 }{ x^{2} - 21 x + 80 }$

$\frac{x^{2} + 16 x}{x - 5}$

$\frac{2 x - 18}{2 x - 21}$

Correct answer:

$\frac{ 2 x^{2} - 39 x + 79 }{ x^{2} - 21 x + 80 }$

Explanation:

The first step we need to take in order to simplify this expression is to find a common denominator.

We do this by multiplying by a clever form of one to each fraction.

$\frac{\left( x + 1 \right) \left( x - 16 \right)}{\left( x - 5 \right) \left( x - 16 \right)}+ \frac{\left( x - 19 \right) \left( x - 5 \right)}{\left( x - 5 \right) \left( x - 16 \right)}$
Now we can use FOIL for the numerator and the denominator.

$=\frac{ x^{2} - 15 x - 16 }{ x^{2} - 21 x + 80 }+ \frac{ x^{2} - 24 x + 95 }{ x^{2} - 21 x + 80 }$
Now we can combine the fractions since they have a common denominator, and put the like terms together.

$=\frac{ x^{2} - 15 x - 16 + x^{2} - 24 x + 95 }{ x^{2} - 21 x + 80 }$

$=\frac{ 2 x^{2} - 39 x + 79 }{ x^{2} - 21 x + 80 }$

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Example Question #332 : Arithmetic With Polynomials & Rational Expressions

Simplify:

$\frac{x}{x - 17} + \frac{x - 10}{x - 3}$

Possible Answers:

$\frac{ 2 x^{2} - 30 x + 170 }{ x^{2} - 20 x + 51 }$

$\frac{2 x - 10}{2 x - 20}$

$\frac{x^{2} + 17 x}{x - 3}$

$\frac{ 2 x^{2} + 7 x + 170 }{ x^{2} - 20 x + 51 }$

$\frac{2 x - 10}{2 x - 20}$

Correct answer:

$\frac{ 2 x^{2} - 30 x + 170 }{ x^{2} - 20 x + 51 }$

Explanation:

The first step we need to take in order to simplify this expression is to find a common denominator.

We do this by multiplying by a clever form of one to each fraction.

$\frac{\left( x - 10 \right) \left( x - 17 \right)}{\left( x - 3 \right) \left( x - 17 \right)}+ \frac{\left( x \right) \left( x - 3 \right)}{\left( x - 3 \right) \left( x - 17 \right)}$
Now we can use FOIL for the numerator and the denominator.

$=\frac{ x^{2} - 27 x + 170 }{ x^{2} - 20 x + 51 }+ \frac{ x^{2} - 3 x }{ x^{2} - 20 x + 51 }$
Now we can combine the fractions since they have a common denominator, and put the like terms together.

$=\frac{ x^{2} - 27 x + 170 + x^{2} - 3 x }{ x^{2} - 20 x + 51 }$

= $\frac{ 2 x^{2} - 30 x + 170 }{ x^{2} - 20 x + 51 }$

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Common Core: High School - Algebra : Rational Expressions: CCSS.Math.Content.HSA-APR.D.7

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #331 : Arithmetic With Polynomials & Rational Expressions

Example Question #332 : Arithmetic With Polynomials & Rational Expressions

All Common Core: High School - Algebra Resources

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