What is the answer to (4x)/(x+1)+2/(x-3)=4 ?

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

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(4x)/(x+1)+2/(x-3)=4

Solution

\frac{4 x}{x + 1} + \frac{2}{x - 3} = 4

Solution

x = 7

Solution steps

\frac{4 x}{x + 1} + \frac{2}{x - 3} = 4

Multiply by LCM

4 x (x - 3) + 2 (x + 1) = 4 (x + 1) (x - 3)

Expand

4 x (x - 3) : 4 x^{2} - 12 x

4 x^{2} - 12 x + 2 (x + 1) = 4 (x + 1) (x - 3)

Expand

2 (x + 1) : 2 x + 2

4 x^{2} - 12 x + 2 x + 2 = 4 (x + 1) (x - 3)

Add similar elements:

- 12 x + 2 x = - 10 x

4 x^{2} - 10 x + 2 = 4 (x + 1) (x - 3)

Expand

(x + 1) (x - 3) : x^{2} - 2 x - 3

4 x^{2} - 10 x + 2 = 4 (x^{2} - 2 x - 3)

Expand

4 (x^{2} - 2 x - 3) : 4 x^{2} - 8 x - 12

4 x^{2} - 10 x + 2 = 4 x^{2} - 8 x - 12

Move

2

to the right side

4 x^{2} - 10 x = 4 x^{2} - 8 x - 14

Subtract

4 x^{2} - 8 x

from both sides

4 x^{2} - 10 x - (4 x^{2} - 8 x) = 4 x^{2} - 8 x - 14 - (4 x^{2} - 8 x)

Simplify

- 2 x = - 14

Divide both sides by

- 2

x = 7

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 3

Combine undefined points with solutions:

x = 7

Popular Examples

(x+5)((90)/x)=90

(x + 5) (\frac{90}{x}) = 90

5/x =80

\frac{5}{x} = 80

4=(2b+8)/(b+24)

4 = \frac{2 b + 8}{b + 24}

-4/x =-1/(x+6)

- \frac{4}{x} = - \frac{1}{x + 6}

(2x-1)/(x-1)=0

\frac{2 x - 1}{x - 1} = 0

Frequently Asked Questions (FAQ)

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

(4x)/(x+1)+2/(x-3)=4

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to (4x)/(x+1)+2/(x-3)=4 ?

Solve for x: (4x)/(x+1)+2/(x-3)=4