Solving rational equations - Rational Equations and Expressions

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.

Basic Concepts
Solving quadratic equations by factoring

Lessons

Notes:

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:
2.
Solving Rational Equations by cross multiplying
State the non-permissible values for the variable x, then solve algebraically.
4.
Solve the following equations algebraically:
5.
Solving Rational Equations by factoring
State the non-permissible values for the variables, then solve algebraically.

Solving rational equations

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Don't just watch, practice makes perfect

Do better in math today

Don't just watch, practice makes perfect

Lessons

Notes:

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)

3−3x=1+1x3-\frac{3}{x}=1+\frac{1}{x} 3−x3​=1+x1​

b)

2x+15x=132x+\frac{15}{x}=13 2x+x15​=13

2.

Solving Rational Equations by cross multiplying State the non-permissible values for the variable x, then solve algebraically.

a)

8x+4=3x−1 \frac{8}{x+4}=\frac{3}{x-1} x+48​=x−13​

b)

2x−26x−1=3x+49x+5 \frac{2x-2}{6x-1}=\frac{3x+4}{9x+5} 6x−12x−2​=9x+53x+4​

3.

Solve 2x−9+20x+9=80x2−81 \frac{2}{x-9}+\frac{20}{x+9}=\frac{80}{x^2-81} x−92​+x+920​=x2−8180​

4.

Solve the following equations algebraically:

a)

2x+2+3x−2=1\frac{2}{x+2}+\frac{3}{x-2}=1 x+22​+x−23​=1

b)

2t−3t−1−3t+1t+2=−1\frac{2t-3}{t-1}-\frac{3t+1}{t+2}=-1 t−12t−3​−t+23t+1​=−1

5.

Solving Rational Equations by factoring State the non-permissible values for the variables, then solve algebraically.

a)

x2−5x+4(x−1)=−4 \frac{x^2-5x+4}{(x-1)}=-4 (x−1)x2−5x+4​=−4

b)

x−1x2−1=12x−3\frac{x-1}{x^2-1}=\frac{1}{2x-3} x2−1x−1​=2x−31​

Solving rational equations

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Algebra
Solving quadratic equations by factoring

or

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

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

Solving Rational Equations by cross multiplying
State the non-permissible values for the variable x, then solve algebraically.

$\frac{8}{x+4}=\frac{3}{x-1}$

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

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

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

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

Solving Rational Equations by factoring
State the non-permissible values for the variables, then solve algebraically.

$\frac{x^2-5x+4}{(x-1)}=-4$

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