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

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

Solve for x

$$x=-\frac{9}{17}\approx -0.529411765$$

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

$$2\left(x+1\right)\times \frac{5}{2}+2\left(x-3\right)=-10\left(x+1\right)$$

Use the distributive property to multiply 2 by x+1.

$$\left(2x+2\right)\times \frac{5}{2}+2\left(x-3\right)=-10\left(x+1\right)$$

Use the distributive property to multiply 2x+2 by \frac{5}{2}.

$$5x+5+2\left(x-3\right)=-10\left(x+1\right)$$

Use the distributive property to multiply 2 by x-3.

$$5x+5+2x-6=-10\left(x+1\right)$$

Combine 5x and 2x to get 7x.

$$7x+5-6=-10\left(x+1\right)$$

Subtract 6 from 5 to get -1.

$$7x-1=-10\left(x+1\right)$$

Use the distributive property to multiply -10 by x+1.

$$7x-1=-10x-10$$

Add 10x to both sides.

$$7x-1+10x=-10$$

Combine 7x and 10x to get 17x.

$$17x-1=-10$$

Add 1 to both sides.

$$17x=-10+1$$

Add -10 and 1 to get -9.

$$17x=-9$$

Divide both sides by 17.

$$x=\frac{-9}{17}$$

Fraction \frac{-9}{17} can be rewritten as -\frac{9}{17} by extracting the negative sign.

$$x=-\frac{9}{17}$$