Solve y=5/2x+3/2/2x-frac{5{2}}

$$y = \frac { \frac { 5 } { 2 } x + \frac { 3 } { 2 } } { 2 x - \frac { 5 } { 2 } }$$

Solve for x

$$x=\frac{5y+3}{4y-5}$$

$$y\neq \frac{5}{4}$$

Steps for Solving Linear Equation

Factor the expressions that are not already factored in \frac{\frac{5}{2}x+\frac{3}{2}}{2x-\frac{5}{2}}.

$$y=\frac{\frac{1}{2}\left(5x+3\right)}{\frac{1}{2}\left(4x-5\right)}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$y=\frac{5x+3}{\left(\frac{1}{2}\right)^{0}\left(4x-5\right)}$$

Calculate \frac{1}{2} to the power of 0 and get 1.

$$y=\frac{5x+3}{1\left(4x-5\right)}$$

Use the distributive property to multiply 1 by 4x-5.

$$y=\frac{5x+3}{4x-5}$$

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

$$\frac{5x+3}{4x-5}=y$$

Variable x cannot be equal to \frac{5}{4} since division by zero is not defined. Multiply both sides of the equation by 4x-5.

$$5x+3=y\left(4x-5\right)$$

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

$$5x+3=4yx-5y$$

Subtract 4yx from both sides.

$$5x+3-4yx=-5y$$

Subtract 3 from both sides.

$$5x-4yx=-5y-3$$

Combine all terms containing x.

$$\left(5-4y\right)x=-5y-3$$

Divide both sides by 5-4y.

$$\frac{\left(5-4y\right)x}{5-4y}=\frac{-5y-3}{5-4y}$$

Dividing by 5-4y undoes the multiplication by 5-4y.

$$x=\frac{-5y-3}{5-4y}$$

Divide -5y-3 by 5-4y.

$$x=-\frac{5y+3}{5-4y}$$

Variable x cannot be equal to \frac{5}{4}.

$$x=-\frac{5y+3}{5-4y}\text{, }x\neq \frac{5}{4}$$

Solve for y

$$y=\frac{5x+3}{4x-5}$$

$$x\neq \frac{5}{4}$$