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

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

Solve for x

$$x=\sqrt{2}\approx 1.414213562$$

$$x=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -3,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+3\right), the least common multiple of x+3,x,x^{2}+3x.

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

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

$$x^{2}-x-\left(x+3\right)\left(2-3\right)=5$$

Subtract 3 from 2 to get -1.

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

Use the distributive property to multiply x+3 by -1.

$$x^{2}-x-\left(-x-3\right)=5$$

To find the opposite of -x-3, find the opposite of each term.

$$x^{2}-x+x+3=5$$

Combine -x and x to get 0.

$$x^{2}+3=5$$

Subtract 3 from both sides.

$$x^{2}=5-3$$

Subtract 3 from 5 to get 2.

$$x^{2}=2$$

Take the square root of both sides of the equation.

$$x=\sqrt{2} x=-\sqrt{2}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -3,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+3\right), the least common multiple of x+3,x,x^{2}+3x.

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

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

$$x^{2}-x-\left(x+3\right)\left(2-3\right)=5$$

Subtract 3 from 2 to get -1.

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

Use the distributive property to multiply x+3 by -1.

$$x^{2}-x-\left(-x-3\right)=5$$

To find the opposite of -x-3, find the opposite of each term.

$$x^{2}-x+x+3=5$$

Combine -x and x to get 0.

$$x^{2}+3=5$$

Subtract 5 from both sides.

$$x^{2}+3-5=0$$

Subtract 5 from 3 to get -2.

$$x^{2}-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)}}{2}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8}}{2}$$

Take the square root of 8.

$$x=\frac{0±2\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{2}}{2} when ± is plus.

$$x=\sqrt{2}$$

Now solve the equation x=\frac{0±2\sqrt{2}}{2} when ± is minus.

$$x=-\sqrt{2}$$

The equation is now solved.

$$x=\sqrt{2} x=-\sqrt{2}$$