Solve 9/4x+4-4/x+1=5

$$\frac { 9 } { 4 x + 4 } - \frac { 4 } { x + 1 } = 5$$

Solve for x

$$x = -\frac{27}{20} = -1\frac{7}{20} = -1.35$$

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 4\left(x+1\right), the least common multiple of 4x+4,x+1.

$$9-4\times 4=20\left(x+1\right)$$

Multiply -4 and 4 to get -16.

$$9-16=20\left(x+1\right)$$

Subtract 16 from 9 to get -7.

$$-7=20\left(x+1\right)$$

Use the distributive property to multiply 20 by x+1.

$$-7=20x+20$$

Swap sides so that all variable terms are on the left hand side.

$$20x+20=-7$$

Subtract 20 from both sides.

$$20x=-7-20$$

Subtract 20 from -7 to get -27.

$$20x=-27$$

Divide both sides by 20.

$$x=\frac{-27}{20}$$

Fraction \frac{-27}{20} can be rewritten as -\frac{27}{20} by extracting the negative sign.

$$x=-\frac{27}{20}$$