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

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

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

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

x = 5

Solution steps

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

Multiply by LCM

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

Expand

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

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

Expand

2 (x + 2) : 2 x + 4

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

Add similar elements:

- 3 x + 2 x = - x

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

Expand

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

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

Move

4

to the right side

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

Subtract

2 x^{2} + x

from both sides

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

Simplify

- 2 x = - 10

Divide both sides by

- 2

x = 5

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = \frac{3}{2}

Combine undefined points with solutions:

x = 5

x (x + 1) + \frac{24}{x ( x + 1 )} = 14

X (\frac{200}{X - 1}) + 10 X = 200

x + \frac{10}{x} = 11

a, b = \frac{a}{1 - a}

\frac{v - 7}{v + 10} = \frac{3}{5}

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