Rational Equations

Solving Rational Equations

By Mr Gleisberg

Rational Equations with more than 2 terms

• The LCD (lowest common denominator) is the combination of all the denominators of the equations. Reduce this if possible.

• Multiply each term/fraction by the LCD

• Cancel any common factors or terms

• Simplify and solve for x.​

​

​When we can't cross multiply, use LCD

​Example

solve for x​

Your turn

Multiple Choice

Step 2:

$$\left(2x\right)\cdot\frac{3}{x}+\left(2x\right)\cdot\frac{5}{2}=\left(2x\right)\cdot\frac{-12}{x}$$  

Multiplying each term of the equation above by the LCD $$2x$$   will create which equation?

• $$6+5x=-24$$  

• $$3x+10=-24x$$  

Multiple Choice

Solve the rational equation.

$$\frac{5}{x}+\frac{8}{3}=1$$  

• $$x=0$$  

• $$x=3$$  

• $$x=9$$  

• $$x=-9$$  

Multiple Choice

What is the LCD of the rational equation

$$\frac{2x}{x-7}+\frac{x}{2}=\frac{5}{x-7}$$  

• $$2\left(x-7\right)\left(x-7\right)$$  

• $$x-7$$  

• $$2\left(x-7\right)$$  

• $$2\left(x-7\right)^2$$  

Multiple Choice

Solve the rational equation

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

• $$x=-3$$  

• $$x=3$$  

• $$x=-1$$  

• $$x=-\frac{3}{2}$$  

Multiple Choice

Solve the rational equation

$$\frac{2x}{x-7}+\frac{x}{2}=\frac{5}{x-7}$$  

• $$x=3,\ x=10$$  

• $$x=2,\ x=-5$$  

• $$x=5,\ x=-2$$  

• $$x=-3,\ x=-10$$

Last one...​

Multiple Choice

What is the LCD of the rational equation

$$\frac{x}{x-2}+\frac{1}{x-4}=\frac{2}{x^2-6x+8}$$  

• $$\left(x-2\right)\left(x-4\right)$$  

• $$x^2-6x+8$$  

Multiple Choice

Solve the rational equation

$$\frac{x}{x-2}+\frac{1}{x-4}=\frac{2}{x^2-6x+8}$$  

• $$x=4,\ x=-1$$  

• $$x=-3,\ x=-4$$  

• $$x=-1$$  

• $$x=-4,\ x=1$$