Solve x-3=11/x-2-5

$$x - 3 = \frac { 11 } { x - 2 } - 5$$

Solve for x

$$x=\sqrt{15}\approx 3.872983346$$

$$x=-\sqrt{15}\approx -3.872983346$$

Steps by Finding Square Root

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

$$\left(x-2\right)x+\left(x-2\right)\left(-3\right)=11+\left(x-2\right)\left(-5\right)$$

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

$$x^{2}-2x+\left(x-2\right)\left(-3\right)=11+\left(x-2\right)\left(-5\right)$$

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

$$x^{2}-2x-3x+6=11+\left(x-2\right)\left(-5\right)$$

Combine -2x and -3x to get -5x.

$$x^{2}-5x+6=11+\left(x-2\right)\left(-5\right)$$

Use the distributive property to multiply x-2 by -5.

$$x^{2}-5x+6=11-5x+10$$

Add 11 and 10 to get 21.

$$x^{2}-5x+6=21-5x$$

Add 5x to both sides.

$$x^{2}-5x+6+5x=21$$

Combine -5x and 5x to get 0.

$$x^{2}+6=21$$

Subtract 6 from both sides.

$$x^{2}=21-6$$

Subtract 6 from 21 to get 15.

$$x^{2}=15$$

Take the square root of both sides of the equation.

$$x=\sqrt{15} x=-\sqrt{15}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

$$\left(x-2\right)x+\left(x-2\right)\left(-3\right)=11+\left(x-2\right)\left(-5\right)$$

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

$$x^{2}-2x+\left(x-2\right)\left(-3\right)=11+\left(x-2\right)\left(-5\right)$$

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

$$x^{2}-2x-3x+6=11+\left(x-2\right)\left(-5\right)$$

Combine -2x and -3x to get -5x.

$$x^{2}-5x+6=11+\left(x-2\right)\left(-5\right)$$

Use the distributive property to multiply x-2 by -5.

$$x^{2}-5x+6=11-5x+10$$

Add 11 and 10 to get 21.

$$x^{2}-5x+6=21-5x$$

Subtract 21 from both sides.

$$x^{2}-5x+6-21=-5x$$

Subtract 21 from 6 to get -15.

$$x^{2}-5x-15=-5x$$

Add 5x to both sides.

$$x^{2}-5x-15+5x=0$$

Combine -5x and 5x to get 0.

$$x^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-15\right)}}{2}$$

Multiply -4 times -15.

$$x=\frac{0±\sqrt{60}}{2}$$

Take the square root of 60.

$$x=\frac{0±2\sqrt{15}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{2} when ± is plus.

$$x=\sqrt{15}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{2} when ± is minus.

$$x=-\sqrt{15}$$

The equation is now solved.

$$x=\sqrt{15} x=-\sqrt{15}$$