Solve 3r-3/r^2+6r-7+4/r+7=3/r-1

$$\frac { 3 r - 3 } { r ^ { 2 } + 6 r - 7 } + \frac { 4 } { r + 7 } = \frac { 3 } { r - 1 }$$

Solve for r

$$r=7$$

Steps for Solving Linear Equation

Variable r cannot be equal to any of the values -7,1 since division by zero is not defined. Multiply both sides of the equation by \left(r-1\right)\left(r+7\right), the least common multiple of r^{2}+6r-7,r+7,r-1.

$$3r-3+\left(r-1\right)\times 4=\left(r+7\right)\times 3$$

Use the distributive property to multiply r-1 by 4.

$$3r-3+4r-4=\left(r+7\right)\times 3$$

Combine 3r and 4r to get 7r.

$$7r-3-4=\left(r+7\right)\times 3$$

Subtract 4 from -3 to get -7.

$$7r-7=\left(r+7\right)\times 3$$

Use the distributive property to multiply r+7 by 3.

$$7r-7=3r+21$$

Subtract 3r from both sides.

$$7r-7-3r=21$$

Combine 7r and -3r to get 4r.

$$4r-7=21$$

Add 7 to both sides.

$$4r=21+7$$

Add 21 and 7 to get 28.

$$4r=28$$

Divide both sides by 4.

$$r=\frac{28}{4}$$

Divide 28 by 4 to get 7.

$$r=7$$