Rational Equations

Rational Equations

I can solve rational algebraic equations.

PRE-ASSESSMENT SKILLS

How much do you know about rational equations?

Multiple Choice

Add the expression and simplify.

 $\frac{5}{18a^4b}+\frac{2}{27a^3b^2c}.$  

•  $\frac{15bc+4a}{54a^4b^2c}$  

•  $\frac{10bc+4a}{54a^4b^2c}$  

•  $\frac{15bc+3a}{54a^4b^2c}$  

•  $\frac{15𝑎𝑐+4𝑏}{54𝑎^4𝑏^2𝑐}$  

Multiple Choice

Subtract the expression

 $\frac{𝑡+3}{𝑡^2−6𝑡+9}\ by\ \ \frac{8𝑡−24}{𝑡^2−9}\ .$  

•  $\frac{−7𝑡+54𝑡^2−63}{𝑡^3−3𝑡^2−9𝑡+27}$  

•  $\frac{7𝑡^2+54𝑡−63}{𝑡^3−3𝑡^2−9𝑡+27}$  

•  $\frac{−7𝑡^2+54𝑡−63}{𝑡^3−3𝑡^2−9𝑡+27}$  

•  $\frac{−7𝑡^2−54𝑡−63}{𝑡^3−3𝑡^2−9𝑡+27}$  

Multiple Choice

Multiply the expression

 $\frac{4x}{3y}$  and  $\frac{3𝑥^2y^2}{10}.$  

•  $\frac{−2𝑥^3y}{5}$  

•  $\frac{2x^3y}{5}$  

•  $\frac{2x^2y}{5}$  

•  $\frac{-2x^2y}{5}$  

Multiple Choice

Simplify,  $\frac{\frac{c}{c^2-4}-\frac{c}{c-2}}{1+\frac{1}{c+2}}.$  

•  $\frac{c^2-c}{c^2+c-6}$  

•  $\frac{-c^2+c}{c^2+c-6}$  

•  $-\frac{c^2-c}{c^2+c-6}$  

•  $\frac{-c^2-c}{c^2+c-6}$  

Multiple Choice

Perform the indicated operation,  $\frac{1}{n-1}-\frac{1}{n^2-2n+1}+n\ .$  

•  $\frac{𝑛^4−2𝑛^3+2𝑛−2}{(𝑛−1)^2}$  

•  $\frac{𝑛^3−2𝑛^2−2𝑛+2}{(𝑛−1)^2}$  

•  $\frac{𝑛^3+2𝑛^2+2𝑛−2}{(𝑛−1)^2}$  

•  $\frac{𝑛^3−2𝑛^2+2𝑛−2}{(𝑛−1)^2}$  

Rational Equations

Example 1

Let's Practice 1

Example 2

Extraneous root - is a root or solution derived from an equation that is not a solution of the original equation. Therefore, you must check all solutions in the original equation when you solve rational equations.

Example 3

Checking

Let's Practice 2

Multiple Choice

Solve the equation.  $\frac{9}{a+3}=1-\frac{a}{a-3}$  

•  $\frac{3}{2}$  

•  $\frac{9}{2}$  

•  $\frac{3}{a-3}$  

• No solution
  

Multiple Choice

Solve the equation.  $\frac{x}{x+1}+\frac{3x+5}{x^2+4x+3}=\frac{2}{x+3}\ .$  

•  $\frac{2x}{x+1}$  

•  $\frac{x}{x+3}$  

• No solution
  

•  $1$  

Solution and Answers

Let's Practice 1 and 2

FA 1.16

Solving Rational Equations

Multiple Choice

5. Solve for a in terms of b.  $\frac{1}{a}-\frac{2}{b+a}=\frac{1}{b-a}$  

•  $a=3b+1$  

•  $a=3b$ 
  

•  $a=\frac{3}{b}$  

•    $a=\frac{b}{3}$  
  

Solving Word Problems Involving Rational Equations

Number Problem

FA 1.17

Solving Number Problem

STUDY IN ADVANCE!

Motion and Work Problem pp. 165-166