# To find the real solutions of equation x x − 2 + 1 x + 2 = 8 x 2 − 4 .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 77RE
To determine

## To find the real solutions of equation xx−2+1x+2=8x2−4 .

Expert Solution

The solution is x=5,2 .

### Explanation of Solution

Given information:

xx2+1x+2=8x24

Formula used:

Properties of fractions:- AC+BC=A+BC .

Distributive property:- a(b+c)=ab+ac

Calculations:

=xx2+1(x+2)=8x24

=x(x+2)(x2)(x+2)+(x2)(x+2)(x2)=8x24 (Re-write in LCD form)

=x2+2x+x2(x+2)(x2)=8x24=x2+3x2x24=8x24

=x2+3x2=8 (denominator is same)

=x2+3x28=0=x2+3x10=0

a=1b=3c=10

x=(3)±(3)24(1)(10)2(1)

x=3±9+402

x=3±492

x=3+72=42=2 and x=372=102=5

The solution of the equation x=2,5 .

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