Solve y=1/-x+4-2

$$y = \frac { 1 } { - x + 4 } - 2$$

Solve for x

$$x=\frac{4y+7}{y+2}$$

$$y\neq -2$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{-x+4}{-x+4}.

$$y=\frac{1}{-x+4}-\frac{2\left(-x+4\right)}{-x+4}$$

Since \frac{1}{-x+4} and \frac{2\left(-x+4\right)}{-x+4} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{1-2\left(-x+4\right)}{-x+4}$$

Do the multiplications in 1-2\left(-x+4\right).

$$y=\frac{1+2x-8}{-x+4}$$

Combine like terms in 1+2x-8.

$$y=\frac{-7+2x}{-x+4}$$

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

$$\frac{-7+2x}{-x+4}=y$$

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by -x+4.

$$-7+2x=y\left(-x+4\right)$$

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

$$-7+2x=-yx+4y$$

Add yx to both sides.

$$-7+2x+yx=4y$$

Add 7 to both sides.

$$2x+yx=4y+7$$

Combine all terms containing x.

$$\left(2+y\right)x=4y+7$$

The equation is in standard form.

$$\left(y+2\right)x=4y+7$$

Divide both sides by y+2.

$$\frac{\left(y+2\right)x}{y+2}=\frac{4y+7}{y+2}$$

Dividing by y+2 undoes the multiplication by y+2.

$$x=\frac{4y+7}{y+2}$$

Variable x cannot be equal to 4.

$$x=\frac{4y+7}{y+2}\text{, }x\neq 4$$

Solve for y

$$y=-\frac{7-2x}{4-x}$$

$$x\neq 4$$