Solve 6+6b-9/b-1=63b/b-1

$$6 + \frac { 6 b - 9 } { b - 1 } = 6 \frac { 3 b } { b - 1 }$$

Solve for b

$$b = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps for Solving Linear Equation

Variable b cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by b-1.

$$\left(b-1\right)\times 6+6b-9=6\times 3b$$

Use the distributive property to multiply b-1 by 6.

$$6b-6+6b-9=6\times 3b$$

Combine 6b and 6b to get 12b.

$$12b-6-9=6\times 3b$$

Subtract 9 from -6 to get -15.

$$12b-15=6\times 3b$$

Multiply 6 and 3 to get 18.

$$12b-15=18b$$

Subtract 18b from both sides.

$$12b-15-18b=0$$

Combine 12b and -18b to get -6b.

$$-6b-15=0$$

Add 15 to both sides. Anything plus zero gives itself.

$$-6b=15$$

Divide both sides by -6.

$$b=\frac{15}{-6}$$

Reduce the fraction \frac{15}{-6} to lowest terms by extracting and canceling out 3.

$$b=-\frac{5}{2}$$