Solve 6/x+1-5/2=6/3x+3

$$\frac { 6 } { x + 1 } - \frac { 5 } { 2 } = \frac { 6 } { 3 x + 3 }$$

Solve for x

$$x=\frac{3}{5}=0.6$$

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 6\left(x+1\right), the least common multiple of x+1,2,3x+3.

$$6\times 6+6\left(x+1\right)\left(-\frac{5}{2}\right)=2\times 6$$

Multiply 6 and 6 to get 36.

$$36+6\left(x+1\right)\left(-\frac{5}{2}\right)=2\times 6$$

Multiply 6 and -\frac{5}{2} to get -15.

$$36-15\left(x+1\right)=2\times 6$$

Use the distributive property to multiply -15 by x+1.

$$36-15x-15=2\times 6$$

Subtract 15 from 36 to get 21.

$$21-15x=2\times 6$$

Multiply 2 and 6 to get 12.

$$21-15x=12$$

Subtract 21 from both sides.

$$-15x=12-21$$

Subtract 21 from 12 to get -9.

$$-15x=-9$$

Divide both sides by -15.

$$x=\frac{-9}{-15}$$

Reduce the fraction \frac{-9}{-15} to lowest terms by extracting and canceling out -3.

$$x=\frac{3}{5}$$