Solving Rational Equations
- To solve simple rational equations, you can use cross multiplication. You can also multiply both sides by the LCM of the two denominators. Shown below, cross multiplication is used to solve.
- \(\dfrac{x-1}{5}=\dfrac{9}{7}\)
- \(\dfrac{x+2}{3}=\dfrac{4}{9}\)
- What about more complicated equations?
Try finding common denominators as a first step in solving the next equations. Once all of the terms have a common denominator, solve the equation created by the numerators.
- \(\dfrac{3}{x+4}+\dfrac{1}{4}= 5\)
- \(\dfrac{x}{x-5}+\dfrac{3}{x+2}=\dfrac{7x}{x^2-3x-10}\)