What is the answer to (x+1)/(x+2)+(x+2)/(x+3)=2 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(x+1)/(x+2)+(x+2)/(x+3)=2

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

x = - \frac{5}{2}

Decimal Notation

x = - 2.5

Solution steps

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

Multiply by LCM

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

Expand

(x + 2) (x + 3) : x^{2} + 5 x + 6

2 x^{2} + 8 x + 7 = 2 (x^{2} + 5 x + 6)

Expand

2 (x^{2} + 5 x + 6) : 2 x^{2} + 10 x + 12

2 x^{2} + 8 x + 7 = 2 x^{2} + 10 x + 12

Expand

(x + 1) (x + 3) + (x + 2)^{2} : 2 x^{2} + 8 x + 7

2 x^{2} + 8 x + 7 = 2 x^{2} + 10 x + 12

Move

7

to the right side

2 x^{2} + 8 x = 2 x^{2} + 10 x + 5

Subtract

2 x^{2} + 10 x

from both sides

2 x^{2} + 8 x - (2 x^{2} + 10 x) = 2 x^{2} + 10 x + 5 - (2 x^{2} + 10 x)

Simplify

- 2 x = 5

Divide both sides by

- 2

x = - \frac{5}{2}

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = - 3

Combine undefined points with solutions:

x = - \frac{5}{2}

\frac{4.2}{3 x} = 7

\frac{2 x - 2}{x ^{2} - 2 x + 2} = 0

\frac{7 x + 2}{14 x - 3} = \frac{x - 8}{2 x + 3}

\frac{5}{x + 3} = \frac{3}{x + 5}

5 = \frac{\frac{x}{150}}{\frac{80 - x}{100}}

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