Solve 3r-3/r^2+3r-18+3/r+6=2/r-3

$$\frac { 3 r - 3 } { r ^ { 2 } + 3 r - 18 } + \frac { 3 } { r + 6 } = \frac { 2 } { r - 3 }$$

Solve for r

$$r=6$$

Steps for Solving Linear Equation

Variable r cannot be equal to any of the values -6,3 since division by zero is not defined. Multiply both sides of the equation by \left(r-3\right)\left(r+6\right), the least common multiple of r^{2}+3r-18,r+6,r-3.

$$3r-3+\left(r-3\right)\times 3=\left(r+6\right)\times 2$$

Use the distributive property to multiply r-3 by 3.

$$3r-3+3r-9=\left(r+6\right)\times 2$$

Combine 3r and 3r to get 6r.

$$6r-3-9=\left(r+6\right)\times 2$$

Subtract 9 from -3 to get -12.

$$6r-12=\left(r+6\right)\times 2$$

Use the distributive property to multiply r+6 by 2.

$$6r-12=2r+12$$

Subtract 2r from both sides.

$$6r-12-2r=12$$

Combine 6r and -2r to get 4r.

$$4r-12=12$$

Add 12 to both sides.

$$4r=12+12$$

Add 12 and 12 to get 24.

$$4r=24$$

Divide both sides by 4.

$$r=\frac{24}{4}$$

Divide 24 by 4 to get 6.

$$r=6$$