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

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

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

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

x = \frac{7}{2}

Decimal Notation

x = 3.5

Solution steps

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

Multiply by LCM

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

Expand

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

3 x^{2} - 5 x + 1 = 3 (x^{2} - x - 2)

Expand

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

3 x^{2} - 5 x + 1 = 3 x^{2} - 3 x - 6

Expand

x + 1 + 3 x (x - 2) : 3 x^{2} - 5 x + 1

3 x^{2} - 5 x + 1 = 3 x^{2} - 3 x - 6

Move

1

to the right side

3 x^{2} - 5 x = 3 x^{2} - 3 x - 7

Subtract

3 x^{2} - 3 x

from both sides

3 x^{2} - 5 x - (3 x^{2} - 3 x) = 3 x^{2} - 3 x - 7 - (3 x^{2} - 3 x)

Simplify

- 2 x = - 7

Divide both sides by

- 2

x = \frac{7}{2}

Verify Solutions

Find undefined (singularity) points:

x = 2, x = - 1

Combine undefined points with solutions:

x = \frac{7}{2}

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

\frac{1}{x} = \frac{1}{a}

\frac{8 x}{x - 5.7} = 20

\frac{6 x - 1}{3 - 2 x} = 5

x^{2} + \frac{432}{x} = 0

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