Solve y^2/y+8=64/y+8

$$\frac { y ^ { 2 } } { y + 8 } = \frac { 64 } { y + 8 }$$

Solve for y

$$y=8$$

Steps Using Difference of Squares

Variable y cannot be equal to -8 since division by zero is not defined. Multiply both sides of the equation by y+8.

$$y^{2}=64$$

Subtract 64 from both sides.

$$y^{2}-64=0$$

Consider y^{2}-64. Rewrite y^{2}-64 as y^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-8\right)\left(y+8\right)=0$$

To find equation solutions, solve y-8=0 and y+8=0.

$$y=8 y=-8$$

Variable y cannot be equal to -8.

$$y=8$$

Steps by Finding Square Root

Variable y cannot be equal to -8 since division by zero is not defined. Multiply both sides of the equation by y+8.

$$y^{2}=64$$

Take the square root of both sides of the equation.

$$y=8 y=-8$$

Variable y cannot be equal to -8.

$$y=8$$

Steps Using the Quadratic Formula

Variable y cannot be equal to -8 since division by zero is not defined. Multiply both sides of the equation by y+8.

$$y^{2}=64$$

Subtract 64 from both sides.

$$y^{2}-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-64\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-64\right)}}{2}$$

Multiply -4 times -64.

$$y=\frac{0±\sqrt{256}}{2}$$

Take the square root of 256.

$$y=\frac{0±16}{2}$$

Now solve the equation y=\frac{0±16}{2} when ± is plus. Divide 16 by 2.

$$y=8$$

Now solve the equation y=\frac{0±16}{2} when ± is minus. Divide -16 by 2.

$$y=-8$$

The equation is now solved.

$$y=8 y=-8$$

Variable y cannot be equal to -8.

$$y=8$$