Solve xleft(4x-62right)+51/x+1=4x-62+4

$$\frac{ x \left( 4x-62 \right) +51 }{ x+1 } = 4x-62+4$$

Solve for x

$$x = \frac{109}{8} = 13\frac{5}{8} = 13.625$$

Steps for Solving Linear Equation

Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by x+1.

$$x\left(4x-62\right)+51=4x\left(x+1\right)+\left(x+1\right)\left(-62\right)+\left(x+1\right)\times 4$$

Use the distributive property to multiply x by 4x-62.

$$4x^{2}-62x+51=4x\left(x+1\right)+\left(x+1\right)\left(-62\right)+\left(x+1\right)\times 4$$

Use the distributive property to multiply 4x by x+1.

$$4x^{2}-62x+51=4x^{2}+4x+\left(x+1\right)\left(-62\right)+\left(x+1\right)\times 4$$

Use the distributive property to multiply x+1 by -62.

$$4x^{2}-62x+51=4x^{2}+4x-62x-62+\left(x+1\right)\times 4$$

Combine 4x and -62x to get -58x.

$$4x^{2}-62x+51=4x^{2}-58x-62+\left(x+1\right)\times 4$$

Use the distributive property to multiply x+1 by 4.

$$4x^{2}-62x+51=4x^{2}-58x-62+4x+4$$

Combine -58x and 4x to get -54x.

$$4x^{2}-62x+51=4x^{2}-54x-62+4$$

Add -62 and 4 to get -58.

$$4x^{2}-62x+51=4x^{2}-54x-58$$

Subtract 4x^{2} from both sides.

$$4x^{2}-62x+51-4x^{2}=-54x-58$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-62x+51=-54x-58$$

Add 54x to both sides.

$$-62x+51+54x=-58$$

Combine -62x and 54x to get -8x.

$$-8x+51=-58$$

Subtract 51 from both sides.

$$-8x=-58-51$$

Subtract 51 from -58 to get -109.

$$-8x=-109$$

Divide both sides by -8.

$$x=\frac{-109}{-8}$$

Fraction \frac{-109}{-8} can be simplified to \frac{109}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{109}{8}$$