Solve 2x-4/x+4=-y/5

$$\frac { 2 x - 4 } { x + 4 } = - \frac { y } { 5 }$$

Solve for x

$$x=-\frac{4\left(y-5\right)}{y+10}$$

$$y\neq -10$$

Steps for Solving Linear Equation

Variable x cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by 5\left(x+4\right), the least common multiple of x+4,5.

$$5\left(2x-4\right)=-\left(x+4\right)y$$

Use the distributive property to multiply 5 by 2x-4.

$$10x-20=-\left(x+4\right)y$$

Use the distributive property to multiply x+4 by y.

$$10x-20=-\left(xy+4y\right)$$

To find the opposite of xy+4y, find the opposite of each term.

$$10x-20=-xy-4y$$

Add xy to both sides.

$$10x-20+xy=-4y$$

Add 20 to both sides.

$$10x+xy=-4y+20$$

Combine all terms containing x.

$$\left(10+y\right)x=-4y+20$$

The equation is in standard form.

$$\left(y+10\right)x=20-4y$$

Divide both sides by y+10.

$$\frac{\left(y+10\right)x}{y+10}=\frac{20-4y}{y+10}$$

Dividing by y+10 undoes the multiplication by y+10.

$$x=\frac{20-4y}{y+10}$$

Divide -4y+20 by y+10.

$$x=\frac{4\left(5-y\right)}{y+10}$$

Variable x cannot be equal to -4.

$$x=\frac{4\left(5-y\right)}{y+10}\text{, }x\neq -4$$

Solve for y

$$y=\frac{10\left(2-x\right)}{x+4}$$

$$x\neq -4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5\left(x+4\right), the least common multiple of x+4,5.

$$5\left(2x-4\right)=-\left(x+4\right)y$$

Use the distributive property to multiply 5 by 2x-4.

$$10x-20=-\left(x+4\right)y$$

Use the distributive property to multiply x+4 by y.

$$10x-20=-\left(xy+4y\right)$$

To find the opposite of xy+4y, find the opposite of each term.

$$10x-20=-xy-4y$$

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

$$-xy-4y=10x-20$$

Combine all terms containing y.

$$\left(-x-4\right)y=10x-20$$

Divide both sides by -x-4.

$$\frac{\left(-x-4\right)y}{-x-4}=\frac{10x-20}{-x-4}$$

Dividing by -x-4 undoes the multiplication by -x-4.

$$y=\frac{10x-20}{-x-4}$$

Divide -20+10x by -x-4.

$$y=-\frac{10\left(x-2\right)}{x+4}$$