Solve 6+6b-9/b-1=3b/b-1

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

Solve for b

$$b = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

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.

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

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

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

Combine 6b and 6b to get 12b.

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

Subtract 9 from -6 to get -15.

$$12b-15=3b$$

Subtract 3b from both sides.

$$12b-15-3b=0$$

Combine 12b and -3b to get 9b.

$$9b-15=0$$

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

$$9b=15$$

Divide both sides by 9.

$$b=\frac{15}{9}$$

Reduce the fraction \frac{15}{9} to lowest terms by extracting and canceling out 3.

$$b=\frac{5}{3}$$