Solve (4a+6)div6/a-2*3/2a^2-3a-2

$$( 4 a + 6 ) \div \frac { 6 } { a - 2 } \times \frac { 3 } { 2 a ^ { 2 } - 3 a - 2 }$$

Evaluate

$$\frac{2a+3}{2a+1}$$

Short Solution Steps

Divide 4a+6 by \frac{6}{a-2} by multiplying 4a+6 by the reciprocal of \frac{6}{a-2}.

$$\frac{\left(4a+6\right)\left(a-2\right)}{6}\times \frac{3}{2a^{2}-3a-2}$$

Multiply \frac{\left(4a+6\right)\left(a-2\right)}{6} times \frac{3}{2a^{2}-3a-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4a+6\right)\left(a-2\right)\times 3}{6\left(2a^{2}-3a-2\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\left(a-2\right)\left(4a+6\right)}{2\left(2a^{2}-3a-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(a-2\right)\left(2a+3\right)}{2\left(a-2\right)\left(2a+1\right)}$$

Cancel out 2\left(a-2\right) in both numerator and denominator.

$$\frac{2a+3}{2a+1}$$

Expand

$$\frac{2a+3}{2a+1}$$

Short Solution Steps

Divide 4a+6 by \frac{6}{a-2} by multiplying 4a+6 by the reciprocal of \frac{6}{a-2}.

$$\frac{\left(4a+6\right)\left(a-2\right)}{6}\times \frac{3}{2a^{2}-3a-2}$$

Multiply \frac{\left(4a+6\right)\left(a-2\right)}{6} times \frac{3}{2a^{2}-3a-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4a+6\right)\left(a-2\right)\times 3}{6\left(2a^{2}-3a-2\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\left(a-2\right)\left(4a+6\right)}{2\left(2a^{2}-3a-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(a-2\right)\left(2a+3\right)}{2\left(a-2\right)\left(2a+1\right)}$$

Cancel out 2\left(a-2\right) in both numerator and denominator.

$$\frac{2a+3}{2a+1}$$