Solve 8xy-24/6x^2-24=y-1/3x+6-2y-2/4-2x

$$\frac { 8 x y - 24 } { 6 x ^ { 2 } - 24 } = \frac { y - 1 } { 3 x + 6 } - \frac { 2 y - 2 } { 4 - 2 x }$$

Solve for x (complex solution)

$$x=y+2$$

$$y\neq -4\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by 6\left(x-2\right)\left(x+2\right), the least common multiple of 6x^{2}-24,3x+6,4-2x.

$$8xy-24=\left(2x-4\right)\left(y-1\right)-\left(-6-3x\right)\left(2y-2\right)$$

Use the distributive property to multiply 2x-4 by y-1.

$$8xy-24=2xy-2x-4y+4-\left(-6-3x\right)\left(2y-2\right)$$

Use the distributive property to multiply -6-3x by 2y-2.

$$8xy-24=2xy-2x-4y+4-\left(-12y+12-6xy+6x\right)$$

To find the opposite of -12y+12-6xy+6x, find the opposite of each term.

$$8xy-24=2xy-2x-4y+4+12y-12+6xy-6x$$

Combine -4y and 12y to get 8y.

$$8xy-24=2xy-2x+8y+4-12+6xy-6x$$

Subtract 12 from 4 to get -8.

$$8xy-24=2xy-2x+8y-8+6xy-6x$$

Combine 2xy and 6xy to get 8xy.

$$8xy-24=8xy-2x+8y-8-6x$$

Combine -2x and -6x to get -8x.

$$8xy-24=8xy-8x+8y-8$$

Subtract 8xy from both sides.

$$8xy-24-8xy=-8x+8y-8$$

Combine 8xy and -8xy to get 0.

$$-24=-8x+8y-8$$

Swap sides so that all variable terms are on the left hand side.

$$-8x+8y-8=-24$$

Subtract 8y from both sides.

$$-8x-8=-24-8y$$

Add 8 to both sides.

$$-8x=-24-8y+8$$

Add -24 and 8 to get -16.

$$-8x=-16-8y$$

The equation is in standard form.

$$-8x=-8y-16$$

Divide both sides by -8.

$$\frac{-8x}{-8}=\frac{-8y-16}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$x=\frac{-8y-16}{-8}$$

Divide -16-8y by -8.

$$x=y+2$$

Variable x cannot be equal to any of the values -2,2.

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

Solve for y (complex solution)

$$y=x-2$$

$$x\neq -2\text{ and }x\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6\left(x-2\right)\left(x+2\right), the least common multiple of 6x^{2}-24,3x+6,4-2x.

$$8xy-24=\left(2x-4\right)\left(y-1\right)-\left(-6-3x\right)\left(2y-2\right)$$

Use the distributive property to multiply 2x-4 by y-1.

$$8xy-24=2xy-2x-4y+4-\left(-6-3x\right)\left(2y-2\right)$$

Use the distributive property to multiply -6-3x by 2y-2.

$$8xy-24=2xy-2x-4y+4-\left(-12y+12-6xy+6x\right)$$

To find the opposite of -12y+12-6xy+6x, find the opposite of each term.

$$8xy-24=2xy-2x-4y+4+12y-12+6xy-6x$$

Combine -4y and 12y to get 8y.

$$8xy-24=2xy-2x+8y+4-12+6xy-6x$$

Subtract 12 from 4 to get -8.

$$8xy-24=2xy-2x+8y-8+6xy-6x$$

Combine 2xy and 6xy to get 8xy.

$$8xy-24=8xy-2x+8y-8-6x$$

Combine -2x and -6x to get -8x.

$$8xy-24=8xy-8x+8y-8$$

Subtract 8xy from both sides.

$$8xy-24-8xy=-8x+8y-8$$

Combine 8xy and -8xy to get 0.

$$-24=-8x+8y-8$$

Swap sides so that all variable terms are on the left hand side.

$$-8x+8y-8=-24$$

Add 8x to both sides.

$$8y-8=-24+8x$$

Add 8 to both sides.

$$8y=-24+8x+8$$

Add -24 and 8 to get -16.

$$8y=-16+8x$$

The equation is in standard form.

$$8y=8x-16$$

Divide both sides by 8.

$$\frac{8y}{8}=\frac{8x-16}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$y=\frac{8x-16}{8}$$

Divide -16+8x by 8.

$$y=x-2$$

Solve for x

$$x=y+2$$

$$y\neq 0\text{ and }y\neq -4$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by 6\left(x-2\right)\left(x+2\right), the least common multiple of 6x^{2}-24,3x+6,4-2x.

$$8xy-24=\left(2x-4\right)\left(y-1\right)-\left(-6-3x\right)\left(2y-2\right)$$

Use the distributive property to multiply 2x-4 by y-1.

$$8xy-24=2xy-2x-4y+4-\left(-6-3x\right)\left(2y-2\right)$$

Use the distributive property to multiply -6-3x by 2y-2.

$$8xy-24=2xy-2x-4y+4-\left(-12y+12-6xy+6x\right)$$

To find the opposite of -12y+12-6xy+6x, find the opposite of each term.

$$8xy-24=2xy-2x-4y+4+12y-12+6xy-6x$$

Combine -4y and 12y to get 8y.

$$8xy-24=2xy-2x+8y+4-12+6xy-6x$$

Subtract 12 from 4 to get -8.

$$8xy-24=2xy-2x+8y-8+6xy-6x$$

Combine 2xy and 6xy to get 8xy.

$$8xy-24=8xy-2x+8y-8-6x$$

Combine -2x and -6x to get -8x.

$$8xy-24=8xy-8x+8y-8$$

Subtract 8xy from both sides.

$$8xy-24-8xy=-8x+8y-8$$

Combine 8xy and -8xy to get 0.

$$-24=-8x+8y-8$$

Swap sides so that all variable terms are on the left hand side.

$$-8x+8y-8=-24$$

Subtract 8y from both sides.

$$-8x-8=-24-8y$$

Add 8 to both sides.

$$-8x=-24-8y+8$$

Add -24 and 8 to get -16.

$$-8x=-16-8y$$

The equation is in standard form.

$$-8x=-8y-16$$

Divide both sides by -8.

$$\frac{-8x}{-8}=\frac{-8y-16}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$x=\frac{-8y-16}{-8}$$

Divide -16-8y by -8.

$$x=y+2$$

Variable x cannot be equal to any of the values -2,2.

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

Solve for y

$$y=x-2$$

$$|x|\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6\left(x-2\right)\left(x+2\right), the least common multiple of 6x^{2}-24,3x+6,4-2x.

$$8xy-24=\left(2x-4\right)\left(y-1\right)-\left(-6-3x\right)\left(2y-2\right)$$

Use the distributive property to multiply 2x-4 by y-1.

$$8xy-24=2xy-2x-4y+4-\left(-6-3x\right)\left(2y-2\right)$$

Use the distributive property to multiply -6-3x by 2y-2.

$$8xy-24=2xy-2x-4y+4-\left(-12y+12-6xy+6x\right)$$

To find the opposite of -12y+12-6xy+6x, find the opposite of each term.

$$8xy-24=2xy-2x-4y+4+12y-12+6xy-6x$$

Combine -4y and 12y to get 8y.

$$8xy-24=2xy-2x+8y+4-12+6xy-6x$$

Subtract 12 from 4 to get -8.

$$8xy-24=2xy-2x+8y-8+6xy-6x$$

Combine 2xy and 6xy to get 8xy.

$$8xy-24=8xy-2x+8y-8-6x$$

Combine -2x and -6x to get -8x.

$$8xy-24=8xy-8x+8y-8$$

Subtract 8xy from both sides.

$$8xy-24-8xy=-8x+8y-8$$

Combine 8xy and -8xy to get 0.

$$-24=-8x+8y-8$$

Swap sides so that all variable terms are on the left hand side.

$$-8x+8y-8=-24$$

Add 8x to both sides.

$$8y-8=-24+8x$$

Add 8 to both sides.

$$8y=-24+8x+8$$

Add -24 and 8 to get -16.

$$8y=-16+8x$$

The equation is in standard form.

$$8y=8x-16$$

Divide both sides by 8.

$$\frac{8y}{8}=\frac{8x-16}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$y=\frac{8x-16}{8}$$

Divide -16+8x by 8.

$$y=x-2$$