What is the answer to (4x^2+6x)/(4x+2)=x+4 ?

The answer to (4x^2+6x)/(4x+2)=x+4 is x=-2/3

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(4x^2+6x)/(4x+2)=x+4

\frac{4 x ^{2} + 6 x}{4 x + 2} = x + 4

x = - \frac{2}{3}

Decimal Notation

x = - 0.66666 \dots

Solution steps

\frac{4 x ^{2} + 6 x}{4 x + 2} = x + 4

Simplify

\frac{4 x ^{2} + 6 x}{4 x + 2} : \frac{x ( 2 x + 3 )}{2 x + 1}

\frac{x ( 2 x + 3 )}{2 x + 1} = x + 4

Multiply both sides by

2 x + 1

x (2 x + 3) = x (2 x + 1) + 4 (2 x + 1)

Expand

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

2 x^{2} + 3 x = 2 x^{2} + x + 4 (2 x + 1)

Expand

4 (2 x + 1) : 8 x + 4

2 x^{2} + 3 x = 2 x^{2} + x + 8 x + 4

Add similar elements:

x + 8 x = 9 x

2 x^{2} + 3 x = 2 x^{2} + 9 x + 4

Expand

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

2 x^{2} + 3 x = 2 x^{2} + 9 x + 4

Subtract

2 x^{2} + 9 x

from both sides

2 x^{2} + 3 x - (2 x^{2} + 9 x) = 2 x^{2} + 9 x + 4 - (2 x^{2} + 9 x)

Simplify

- 6 x = 4

Divide both sides by

- 6

x = - \frac{2}{3}

Verify Solutions

Find undefined (singularity) points:

x = - \frac{1}{2}

Combine undefined points with solutions:

x = - \frac{2}{3}

\frac{36000}{r} = 400

x^{- 1} = x

\frac{1}{a - 1} + \frac{3}{3 a - 1} = 0

15 - (\frac{3750}{x ^{2}}) = 0

x, r = \frac{a - x}{a + x}

What is the answer to (4x^2+6x)/(4x+2)=x+4 ?
The answer to (4x^2+6x)/(4x+2)=x+4 is x=-2/3
Solve for x: (4x^2+6x)/(4x+2)=x+4
The solution is x=-2/3