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

The answer to 2/((x+2))+3/((x-1))= 1/((x+2)) is x=-5/4

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

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

x = - \frac{5}{4}

Decimal Notation

x = - 1.25

Solution steps

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

Multiply by LCM

5 x + 4 = x - 1

Move

4

to the right side

5 x = x - 5

Move

x

to the left side

4 x = - 5

Divide both sides by

4

x = - \frac{5}{4}

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 1

Combine undefined points with solutions:

x = - \frac{5}{4}

x^{2} + \frac{1}{( x ^{2} )} + x - \frac{1}{x} - 14 = 0

x^{2} + \frac{1}{( x ^{2} )} = x^{8} + \frac{1}{( x ^{8} )}

\frac{( x - 2 )}{( x + 1 )} = \frac{1}{2}

\frac{3}{5} + \frac{3}{( 2 x - 1 )} = 0

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

What is the answer to 2/((x+2))+3/((x-1))= 1/((x+2)) ?
The answer to 2/((x+2))+3/((x-1))= 1/((x+2)) is x=-5/4
Solve for x: 2/((x+2))+3/((x-1))= 1/((x+2))
The solution is x=-5/4