Solve a/y-4=3+y-2/4-y

$$\frac { a } { y - 4 } = 3 + \frac { y - 2 } { 4 - y }$$

Solve for a

$$a=2\left(y-5\right)$$

$$y\neq 4$$

Solution Steps

Multiply both sides of the equation by y-4, the least common multiple of y-4,4-y.

$$a=\left(y-4\right)\times 3-\left(y-2\right)$$

Use the distributive property to multiply y-4 by 3.

$$a=3y-12-\left(y-2\right)$$

To find the opposite of y-2, find the opposite of each term.

$$a=3y-12-y+2$$

Combine 3y and -y to get 2y.

$$a=2y-12+2$$

Add -12 and 2 to get -10.

$$a=2y-10$$

Solve for y

$$y=\frac{a+10}{2}$$

$$a\neq -2$$

Steps for Solving Linear Equation

Variable y cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by y-4, the least common multiple of y-4,4-y.

$$a=\left(y-4\right)\times 3-\left(y-2\right)$$

Use the distributive property to multiply y-4 by 3.

$$a=3y-12-\left(y-2\right)$$

To find the opposite of y-2, find the opposite of each term.

$$a=3y-12-y+2$$

Combine 3y and -y to get 2y.

$$a=2y-12+2$$

Add -12 and 2 to get -10.

$$a=2y-10$$

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

$$2y-10=a$$

Add 10 to both sides.

$$2y=a+10$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{a+10}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{a+10}{2}$$

Divide a+10 by 2.

$$y=\frac{a}{2}+5$$

Variable y cannot be equal to 4.

$$y=\frac{a}{2}+5\text{, }y\neq 4$$