Solve y=1/x+10-4

$$y = \frac { 1 } { x + 10 } - 4$$

Solve for x

$$x=-\frac{10y+39}{y+4}$$

$$y\neq -4$$

Steps for Solving Linear Equation

Variable x cannot be equal to -10 since division by zero is not defined. Multiply both sides of the equation by x+10.

$$y\left(x+10\right)=1+\left(x+10\right)\left(-4\right)$$

Use the distributive property to multiply y by x+10.

$$yx+10y=1+\left(x+10\right)\left(-4\right)$$

Use the distributive property to multiply x+10 by -4.

$$yx+10y=1-4x-40$$

Subtract 40 from 1 to get -39.

$$yx+10y=-39-4x$$

Add 4x to both sides.

$$yx+10y+4x=-39$$

Subtract 10y from both sides.

$$yx+4x=-39-10y$$

Combine all terms containing x.

$$\left(y+4\right)x=-39-10y$$

The equation is in standard form.

$$\left(y+4\right)x=-10y-39$$

Divide both sides by y+4.

$$\frac{\left(y+4\right)x}{y+4}=\frac{-10y-39}{y+4}$$

Dividing by y+4 undoes the multiplication by y+4.

$$x=\frac{-10y-39}{y+4}$$

Divide -39-10y by y+4.

$$x=-\frac{10y+39}{y+4}$$

Variable x cannot be equal to -10.

$$x=-\frac{10y+39}{y+4}\text{, }x\neq -10$$

Solve for y

$$y=-\frac{4x+39}{x+10}$$

$$x\neq -10$$