Solve x-2/x+2=y-7/y-5

$$\frac { x - 2 } { x + 2 } = \frac { y - 7 } { y - 5 }$$

Solve for x

$$x=2\left(y-6\right)$$

$$y\neq 5$$

Steps for Solving Linear Equation

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

$$\left(y-5\right)\left(x-2\right)=\left(x+2\right)\left(y-7\right)$$

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

$$yx-2y-5x+10=\left(x+2\right)\left(y-7\right)$$

Use the distributive property to multiply x+2 by y-7.

$$yx-2y-5x+10=xy-7x+2y-14$$

Subtract xy from both sides.

$$yx-2y-5x+10-xy=-7x+2y-14$$

Combine yx and -xy to get 0.

$$-2y-5x+10=-7x+2y-14$$

Add 7x to both sides.

$$-2y-5x+10+7x=2y-14$$

Combine -5x and 7x to get 2x.

$$-2y+2x+10=2y-14$$

Add 2y to both sides.

$$2x+10=2y-14+2y$$

Combine 2y and 2y to get 4y.

$$2x+10=4y-14$$

Subtract 10 from both sides.

$$2x=4y-14-10$$

Subtract 10 from -14 to get -24.

$$2x=4y-24$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{4y-24}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{4y-24}{2}$$

Divide -24+4y by 2.

$$x=2y-12$$

Variable x cannot be equal to -2.

$$x=2y-12\text{, }x\neq -2$$

Solve for y

$$y=\frac{x+12}{2}$$

$$x\neq -2$$

Steps for Solving Linear Equation

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

$$\left(y-5\right)\left(x-2\right)=\left(x+2\right)\left(y-7\right)$$

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

$$yx-2y-5x+10=\left(x+2\right)\left(y-7\right)$$

Use the distributive property to multiply x+2 by y-7.

$$yx-2y-5x+10=xy-7x+2y-14$$

Subtract xy from both sides.

$$yx-2y-5x+10-xy=-7x+2y-14$$

Combine yx and -xy to get 0.

$$-2y-5x+10=-7x+2y-14$$

Subtract 2y from both sides.

$$-2y-5x+10-2y=-7x-14$$

Combine -2y and -2y to get -4y.

$$-4y-5x+10=-7x-14$$

Add 5x to both sides.

$$-4y+10=-7x-14+5x$$

Combine -7x and 5x to get -2x.

$$-4y+10=-2x-14$$

Subtract 10 from both sides.

$$-4y=-2x-14-10$$

Subtract 10 from -14 to get -24.

$$-4y=-2x-24$$

Divide both sides by -4.

$$\frac{-4y}{-4}=\frac{-2x-24}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$y=\frac{-2x-24}{-4}$$

Divide -2x-24 by -4.

$$y=\frac{x}{2}+6$$

Variable y cannot be equal to 5.

$$y=\frac{x}{2}+6\text{, }y\neq 5$$