What is the answer to x/(x+2)+6/(x+4)=1 ?

The answer to x/(x+2)+6/(x+4)=1 is x=-1

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x/(x+2)+6/(x+4)=1

\frac{x}{x + 2} + \frac{6}{x + 4} = 1

x = - 1

Solution steps

\frac{x}{x + 2} + \frac{6}{x + 4} = 1

Multiply by LCM

x (x + 4) + 6 (x + 2) = (x + 2) (x + 4)

Expand

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

x^{2} + 4 x + 6 (x + 2) = (x + 2) (x + 4)

Expand

6 (x + 2) : 6 x + 12

x^{2} + 4 x + 6 x + 12 = (x + 2) (x + 4)

Add similar elements:

4 x + 6 x = 10 x

x^{2} + 10 x + 12 = (x + 2) (x + 4)

Expand

(x + 2) (x + 4) : x^{2} + 6 x + 8

x^{2} + 10 x + 12 = x^{2} + 6 x + 8

Move

12

to the right side

x^{2} + 10 x = x^{2} + 6 x - 4

Subtract

x^{2} + 6 x

from both sides

x^{2} + 10 x - (x^{2} + 6 x) = x^{2} + 6 x - 4 - (x^{2} + 6 x)

Simplify

4 x = - 4

Divide both sides by

4

x = - 1

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = - 4

Combine undefined points with solutions:

x = - 1

\frac{6 x - 1}{x ^{2} + 7} = 1

1 + \frac{9}{x ^{2}} = 0

0 = - 1 + \frac{900}{( p + 10 ) ^{2}}

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

\frac{5 x - 12}{3 x - 17} = 4

What is the answer to x/(x+2)+6/(x+4)=1 ?
The answer to x/(x+2)+6/(x+4)=1 is x=-1
Solve for x: x/(x+2)+6/(x+4)=1
The solution is x=-1