Solve 4/y+5+5/25-y^2=9/y-5

$$\frac { 4 } { y + 5 } + \frac { 5 } { 25 - y ^ { 2 } } = \frac { 9 } { y - 5 }$$

Solve for y

$$y=-14$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -5,5 since division by zero is not defined. Multiply both sides of the equation by \left(y-5\right)\left(y+5\right), the least common multiple of y+5,25-y^{2},y-5.

$$\left(y-5\right)\times 4-5=\left(y+5\right)\times 9$$

Use the distributive property to multiply y-5 by 4.

$$4y-20-5=\left(y+5\right)\times 9$$

Subtract 5 from -20 to get -25.

$$4y-25=\left(y+5\right)\times 9$$

Use the distributive property to multiply y+5 by 9.

$$4y-25=9y+45$$

Subtract 9y from both sides.

$$4y-25-9y=45$$

Combine 4y and -9y to get -5y.

$$-5y-25=45$$

Add 25 to both sides.

$$-5y=45+25$$

Add 45 and 25 to get 70.

$$-5y=70$$

Divide both sides by -5.

$$y=\frac{70}{-5}$$

Divide 70 by -5 to get -14.

$$y=-14$$