What is the answer to (5(2x+1)^2)/(4x+5)=5x-1 ?

The answer to (5(2x+1)^2)/(4x+5)=5x-1 is x=10

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(5(2x+1)^2)/(4x+5)=5x-1

\frac{5 ( 2 x + 1 ) ^{2}}{4 x + 5} = 5 x - 1

x = 10

Solution steps

\frac{5 ( 2 x + 1 ) ^{2}}{4 x + 5} = 5 x - 1

Multiply both sides by

4 x + 5

5 (2 x + 1)^{2} = 5 x (4 x + 5) - (4 x + 5)

Expand

5 (2 x + 1)^{2} : 20 x^{2} + 20 x + 5

Expand

5 x (4 x + 5) - (4 x + 5) : 20 x^{2} + 21 x - 5

20 x^{2} + 20 x + 5 = 20 x^{2} + 21 x - 5

Move

5

to the right side

20 x^{2} + 20 x = 20 x^{2} + 21 x - 10

Subtract

20 x^{2} + 21 x

from both sides

20 x^{2} + 20 x - (20 x^{2} + 21 x) = 20 x^{2} + 21 x - 10 - (20 x^{2} + 21 x)

Simplify

- x = - 10

Divide both sides by

- 1

x = 10

Verify Solutions

Find undefined (singularity) points:

x = - \frac{5}{4}

Combine undefined points with solutions:

x = 10

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

y, x = \frac{y + 2}{y - 2}

\frac{36}{b} = 1.3

\frac{12}{6} = \frac{8}{x}

0 = \frac{1}{x - 3}

What is the answer to (5(2x+1)^2)/(4x+5)=5x-1 ?
The answer to (5(2x+1)^2)/(4x+5)=5x-1 is x=10
Solve for x: (5(2x+1)^2)/(4x+5)=5x-1
The solution is x=10