Solve 2r-2/r^2+3r-18+4/r+6=1/r-3

$$\frac { 2 r - 2 } { r ^ { 2 } + 3 r - 18 } + \frac { 4 } { r + 6 } = \frac { 1 } { r - 3 }$$

Solve for r

$$r=4$$

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.

$$2r-2+\left(r-3\right)\times 4=r+6$$

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

$$2r-2+4r-12=r+6$$

Combine 2r and 4r to get 6r.

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

Subtract 12 from -2 to get -14.

$$6r-14=r+6$$

Subtract r from both sides.

$$6r-14-r=6$$

Combine 6r and -r to get 5r.

$$5r-14=6$$

Add 14 to both sides.

$$5r=6+14$$

Add 6 and 14 to get 20.

$$5r=20$$

Divide both sides by 5.

$$r=\frac{20}{5}$$

Divide 20 by 5 to get 4.

$$r=4$$