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

The answer to (3x)/(x+1)+4/(x-2)=3 is x=-10

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

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

x = - 10

Solution steps

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

Multiply by LCM

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

Expand

3 x (x - 2) : 3 x^{2} - 6 x

3 x^{2} - 6 x + 4 (x + 1) = 3 (x + 1) (x - 2)

Expand

4 (x + 1) : 4 x + 4

3 x^{2} - 6 x + 4 x + 4 = 3 (x + 1) (x - 2)

Add similar elements:

- 6 x + 4 x = - 2 x

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

Expand

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

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

Expand

3 (x^{2} - x - 2) : 3 x^{2} - 3 x - 6

3 x^{2} - 2 x + 4 = 3 x^{2} - 3 x - 6

Move

4

to the right side

3 x^{2} - 2 x = 3 x^{2} - 3 x - 10

Subtract

3 x^{2} - 3 x

from both sides

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

Simplify

x = - 10

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 2

Combine undefined points with solutions:

x = - 10

\frac{1}{a} + \frac{2}{5} = \frac{1}{2}

\frac{4 x}{3 x + 5} + \frac{3 x - 1}{2 + 1} = 1

\frac{7}{5} = \frac{28}{x}

- \frac{4 x + 8}{x ^{2} - 9} = \frac{5 x + 1}{x + 3}

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

What is the answer to (3x)/(x+1)+4/(x-2)=3 ?
The answer to (3x)/(x+1)+4/(x-2)=3 is x=-10
Solve for x: (3x)/(x+1)+4/(x-2)=3
The solution is x=-10