What is the answer to 1/((x+1))+3/((x+4))= 4/((x+3)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1/((x+1))+3/((x+4))= 4/((x+3))

\frac{1}{( x + 1 )} + \frac{3}{( x + 4 )} = \frac{4}{( x + 3 )}

x = 5

Solution steps

\frac{1}{( x + 1 )} + \frac{3}{( x + 4 )} = \frac{4}{( x + 3 )}

Multiply by LCM

(x + 4) (x + 3) + 3 (x + 1) (x + 3) = 4 (x + 1) (x + 4)

Expand

(x + 1) (x + 4) : x^{2} + 5 x + 4

4 x^{2} + 19 x + 21 = 4 (x^{2} + 5 x + 4)

Expand

4 (x^{2} + 5 x + 4) : 4 x^{2} + 20 x + 16

4 x^{2} + 19 x + 21 = 4 x^{2} + 20 x + 16

Expand

(x + 4) (x + 3) + 3 (x + 1) (x + 3) : 4 x^{2} + 19 x + 21

4 x^{2} + 19 x + 21 = 4 x^{2} + 20 x + 16

Move

21

to the right side

4 x^{2} + 19 x = 4 x^{2} + 20 x - 5

Subtract

4 x^{2} + 20 x

from both sides

4 x^{2} + 19 x - (4 x^{2} + 20 x) = 4 x^{2} + 20 x - 5 - (4 x^{2} + 20 x)

Simplify

- x = - 5

Divide both sides by

- 1

x = 5

Verify Solutions

Find undefined (singularity) points:

x = - 4, x = - 1, x = - 3

Combine undefined points with solutions:

x = 5

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

\frac{\frac{9}{5}}{x} = \frac{( \frac{3}{2} + \frac{1}{4} )}{( 1 + \frac{7}{9} )}

\frac{a}{x - 51} = 3

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

\frac{- 40}{x + 2} = \frac{- 30}{x}

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