# Solving rational equations

### Solving rational equations

In this lesson, we will learn how to state the non-permissible value(s) of rational equations and how to solve them algebraically.

#### Lessons

Always find the non-permissible values before solving the rational equations as some answers might have to be rejected.
• 1.
Solve the following rational equations:
a)
$3-\frac{3}{x}=1+\frac{1}{x}$

b)
$2x+\frac{15}{x}=13$

• 2.
Solving Rational Equations by cross multiplying
State the non-permissible values for the variable x, then solve algebraically.
a)
$\frac{8}{x+4}=\frac{3}{x-1}$

b)
$\frac{2x-2}{6x-1}=\frac{3x+4}{9x+5}$

• 3.
Solve
$\frac{2}{x-9}+\frac{20}{x+9}=\frac{80}{x^2-81}$

• 4.
Solve the following equations algebraically:
a)
$\frac{2}{x+2}+\frac{3}{x-2}=1$

b)
$\frac{2t-3}{t-1}-\frac{3t+1}{t+2}=-1$

• 5.
Solving Rational Equations by factoring
State the non-permissible values for the variables, then solve algebraically.
a)
$\frac{x^2-5x+4}{(x-1)}=-4$

b)
$\frac{x-1}{x^2-1}=\frac{1}{2x-3}$