What is the answer to 2/(x+1)+3/x = 5/(x-2) ?

The answer to 2/(x+1)+3/x = 5/(x-2) is x=-1/2

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2/(x+1)+3/x = 5/(x-2)

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

x = - \frac{1}{2}

Decimal

x = - 0.5

Solution steps

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

Multiply by LCM

5 x^{2} - 7 x - 6 = 5 x^{2} + 5 x

Move

6

to the right side

5 x^{2} - 7 x = 5 x^{2} + 5 x + 6

Subtract

5 x^{2} + 5 x

from both sides

5 x^{2} - 7 x - (5 x^{2} + 5 x) = 5 x^{2} + 5 x + 6 - (5 x^{2} + 5 x)

Simplify

- 12 x = 6

Divide both sides by

- 12

x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0, x = 2

Combine undefined points with solutions:

x = - \frac{1}{2}

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

\frac{y ^{2}}{y + 4} = \frac{16}{y + 4}

\frac{8}{q} + 2 = \frac{q + 4}{q - 1}

\frac{1}{8} + \frac{1}{x} = \frac{1}{2}

2 x + \frac{16}{x ^{2}} = 0

What is the answer to 2/(x+1)+3/x = 5/(x-2) ?
The answer to 2/(x+1)+3/x = 5/(x-2) is x=-1/2
Solve for x: 2/(x+1)+3/x = 5/(x-2)
The solution is x=-1/2