Solve y-3/y-5=y-1/y-7

$$\frac { y - 3 } { y - 5 } = \frac { y - 1 } { y - 7 }$$

Solve for y

$$y=4$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values 5,7 since division by zero is not defined. Multiply both sides of the equation by \left(y-7\right)\left(y-5\right), the least common multiple of y-5,y-7.

$$\left(y-7\right)\left(y-3\right)=\left(y-5\right)\left(y-1\right)$$

Use the distributive property to multiply y-7 by y-3 and combine like terms.

$$y^{2}-10y+21=\left(y-5\right)\left(y-1\right)$$

Use the distributive property to multiply y-5 by y-1 and combine like terms.

$$y^{2}-10y+21=y^{2}-6y+5$$

Subtract y^{2} from both sides.

$$y^{2}-10y+21-y^{2}=-6y+5$$

Combine y^{2} and -y^{2} to get 0.

$$-10y+21=-6y+5$$

Add 6y to both sides.

$$-10y+21+6y=5$$

Combine -10y and 6y to get -4y.

$$-4y+21=5$$

Subtract 21 from both sides.

$$-4y=5-21$$

Subtract 21 from 5 to get -16.

$$-4y=-16$$

Divide both sides by -4.

$$y=\frac{-16}{-4}$$

Divide -16 by -4 to get 4.

$$y=4$$