Solve 5h+2x-3+2y/y+3=u

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

Solve for h

$$h=-\frac{2xy+6x-uy-2y-3u-3}{5\left(y+3\right)}$$

$$y\neq -3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y+3.

$$5h\left(y+3\right)+2x\left(y+3\right)-\left(3+2y\right)=u\left(y+3\right)$$

Use the distributive property to multiply 5h by y+3.

$$5hy+15h+2x\left(y+3\right)-\left(3+2y\right)=u\left(y+3\right)$$

Use the distributive property to multiply 2x by y+3.

$$5hy+15h+2xy+6x-\left(3+2y\right)=u\left(y+3\right)$$

To find the opposite of 3+2y, find the opposite of each term.

$$5hy+15h+2xy+6x-3-2y=u\left(y+3\right)$$

Use the distributive property to multiply u by y+3.

$$5hy+15h+2xy+6x-3-2y=uy+3u$$

Subtract 2xy from both sides.

$$5hy+15h+6x-3-2y=uy+3u-2xy$$

Subtract 6x from both sides.

$$5hy+15h-3-2y=uy+3u-2xy-6x$$

Add 3 to both sides.

$$5hy+15h-2y=uy+3u-2xy-6x+3$$

Add 2y to both sides.

$$5hy+15h=uy+3u-2xy-6x+3+2y$$

Combine all terms containing h.

$$\left(5y+15\right)h=uy+3u-2xy-6x+3+2y$$

The equation is in standard form.

$$\left(5y+15\right)h=3+3u+2y+uy-6x-2xy$$

Divide both sides by 5y+15.

$$\frac{\left(5y+15\right)h}{5y+15}=\frac{3+3u+2y+uy-6x-2xy}{5y+15}$$

Dividing by 5y+15 undoes the multiplication by 5y+15.

$$h=\frac{3+3u+2y+uy-6x-2xy}{5y+15}$$

Divide uy+3u-2xy-6x+3+2y by 5y+15.

$$h=\frac{3+3u+2y+uy-6x-2xy}{5\left(y+3\right)}$$

Solve for u

$$u=\frac{2xy+6x+5hy-2y+15h-3}{y+3}$$

$$y\neq -3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y+3.

$$5h\left(y+3\right)+2x\left(y+3\right)-\left(3+2y\right)=u\left(y+3\right)$$

Use the distributive property to multiply 5h by y+3.

$$5hy+15h+2x\left(y+3\right)-\left(3+2y\right)=u\left(y+3\right)$$

Use the distributive property to multiply 2x by y+3.

$$5hy+15h+2xy+6x-\left(3+2y\right)=u\left(y+3\right)$$

To find the opposite of 3+2y, find the opposite of each term.

$$5hy+15h+2xy+6x-3-2y=u\left(y+3\right)$$

Use the distributive property to multiply u by y+3.

$$5hy+15h+2xy+6x-3-2y=uy+3u$$

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

$$uy+3u=5hy+15h+2xy+6x-3-2y$$

Combine all terms containing u.

$$\left(y+3\right)u=5hy+15h+2xy+6x-3-2y$$

The equation is in standard form.

$$\left(y+3\right)u=2xy+6x+5hy-2y+15h-3$$

Divide both sides by y+3.

$$\frac{\left(y+3\right)u}{y+3}=\frac{2xy+6x+5hy-2y+15h-3}{y+3}$$

Dividing by y+3 undoes the multiplication by y+3.

$$u=\frac{2xy+6x+5hy-2y+15h-3}{y+3}$$