Week 15 – Solving Rational Equations

One method for solving rational equations is to cross multiply. However, cross-multiplying only works with two fractions.

Ex. $\frac{3x}{4}= \frac{1}{2}$

Multiply the numerator of the first fraction by the denominator of the second fraction. Then multiply the numerator of the second fraction by the denominator of the first fraction.

$3x(2) = 1(4)$ ,

$6x = 4$ ,

$x = \frac{4}{6}=\frac{2}{3}$

Another way of solving rational equations is by multiplying both sides of the equation by a common denominator.

Ex. $\frac{5}{x+4}= \frac{3}{x-2}$

The non-permissible values are $x\neq -4$ and $x\neq 2$

A common denominator is (x + 4)(x – 2). So, multiply each side by (x + 4)(x – 2).

$(x+4)(x-2)\frac{5}{x+4}= (x+4)(x-2)\frac{3}{x-2}$

The (x + 4) cancel each other out on the left side and the (x – 2) cancel each other out on the right side.

We are left with: $(x-2)(5)=(x+4)(3)$

$5x-10=3x+12$

$2x=22$ ,

$x = 11$

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Week 15 – Solving Rational Equations

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