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Algebra 1 : How to find the solution to a rational equation with LCD

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Example Question #11 : How To Find The Solution To A Rational Equation With Lcd

Find the solution: $x=\frac{3}{x}+\frac{1}{2}$ $\displaystyle x=\frac{3}{x}+\frac{1}{2}$

Possible Answers:

$x=-\frac{3}{2}$ $\displaystyle x=-\frac{3}{2}$

x=-2 $\displaystyle x=-2$

$x=\frac{3}{2}$ $\displaystyle x=\frac{3}{2}$

x=2 $\displaystyle x=2$

$x=\frac{3}{2}$ $\displaystyle x=\frac{3}{2}$

x=-2 $\displaystyle x=-2$

$x=-\frac{3}{2}$ $\displaystyle x=-\frac{3}{2}$

x=2 $\displaystyle x=2$

None of these

Correct answer:

$x=-\frac{3}{2}$ $\displaystyle x=-\frac{3}{2}$

x=2 $\displaystyle x=2$

Explanation:

$x=\frac{3}{x}+\frac{1}{2}$ $\displaystyle x=\frac{3}{x}+\frac{1}{2}$

Multiply both sides by 2x:

$(2x)x=(2x)\frac{3}{x}+\frac{1}{2}(2x)$ $\displaystyle (2x)x=(2x)\frac{3}{x}+\frac{1}{2}(2x)$

$\displaystyle 2x^2=6+x$

Move all terms to one side:

$\displaystyle 2x^2-x-6=0$

Solve the quadratic:

$\displaystyle (2x+3)(x-2)=0$

$2x+3=0\rightarrow \mathbf{x=-\frac{3}{2}}$ $\displaystyle 2x+3=0\rightarrow \mathbf{x=-\frac{3}{2}}$

$x-2=0\rightarrow \mathbf{x=2}$ $\displaystyle x-2=0\rightarrow \mathbf{x=2}$

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Algebra 1 : How to find the solution to a rational equation with LCD

Study concepts, example questions & explanations for Algebra 1

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Example Question #11 : How To Find The Solution To A Rational Equation With Lcd

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