Solve 3/2b-5-4/b-3=0

$$\frac { 3 } { 2 b - 5 } - \frac { 4 } { b - 3 } = 0$$

Solve for b

$$b = \frac{11}{5} = 2\frac{1}{5} = 2.2$$

Steps for Solving Linear Equation

Variable b cannot be equal to any of the values \frac{5}{2},3 since division by zero is not defined. Multiply both sides of the equation by \left(b-3\right)\left(2b-5\right), the least common multiple of 2b-5,b-3.

$$\left(b-3\right)\times 3-\left(2b-5\right)\times 4=0$$

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

$$3b-9-\left(2b-5\right)\times 4=0$$

Use the distributive property to multiply 2b-5 by 4.

$$3b-9-\left(8b-20\right)=0$$

To find the opposite of 8b-20, find the opposite of each term.

$$3b-9-8b+20=0$$

Combine 3b and -8b to get -5b.

$$-5b-9+20=0$$

Add -9 and 20 to get 11.

$$-5b+11=0$$

Subtract 11 from both sides. Anything subtracted from zero gives its negation.

$$-5b=-11$$

Divide both sides by -5.

$$b=\frac{-11}{-5}$$

Fraction \frac{-11}{-5} can be simplified to \frac{11}{5} by removing the negative sign from both the numerator and the denominator.

$$b=\frac{11}{5}$$