What is the answer to ((2+x)(x-7))/((x-5)(x+4))=1 ?

The answer to ((2+x)(x-7))/((x-5)(x+4))=1 is x= 3/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

((2+x)(x-7))/((x-5)(x+4))=1

\frac{( 2 + x ) ( x - 7 )}{( x - 5 ) ( x + 4 )} = 1

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

\frac{( 2 + x ) ( x - 7 )}{( x - 5 ) ( x + 4 )} = 1

Multiply both sides by

(x - 5) (x + 4)

(2 + x) (x - 7) = (x - 5) (x + 4)

Expand

(2 + x) (x - 7) : - 5 x + x^{2} - 14

Expand

(x - 5) (x + 4) : x^{2} - x - 20

- 5 x + x^{2} - 14 = x^{2} - x - 20

Move

14

to the right side

- 5 x + x^{2} = x^{2} - x - 6

Subtract

x^{2} - x

from both sides

- 5 x + x^{2} - (x^{2} - x) = x^{2} - x - 6 - (x^{2} - x)

Simplify

- 4 x = - 6

Divide both sides by

- 4

x = \frac{3}{2}

Verify Solutions

Find undefined (singularity) points:

x = 5, x = - 4

Combine undefined points with solutions:

x = \frac{3}{2}

4 \frac{x ^{2}}{x} - 1 - 1 - 3 \frac{x}{4} = 20 \frac{x}{3}

\frac{x ^{2} + x ^{2}}{( x + 1 ) ^{2}} = 3

\frac{3}{7 + x} = \frac{17}{7}

\frac{x ^{3} - 8 x ^{3}}{( x + 2 ) ^{3}} = 7

x + \frac{1}{x} = 5, x^{2} + \frac{1}{( x ^{2} )} =, x^{3} + \frac{1}{( x ^{3} )}

What is the answer to ((2+x)(x-7))/((x-5)(x+4))=1 ?
The answer to ((2+x)(x-7))/((x-5)(x+4))=1 is x= 3/2
Solve for x: ((2+x)(x-7))/((x-5)(x+4))=1
The solution is x= 3/2