Solve 3/-2-3a+2div2/2a^2-5a

$$\frac { 3 } { - 2 - 3 a + 2 } \div \frac { 2 } { 2 a ^ { 2 } - 5 a }$$

Evaluate

$$\frac{5}{2}-a$$

Short Solution Steps

Divide \frac{3}{-2-3a+2} by \frac{2}{2a^{2}-5a} by multiplying \frac{3}{-2-3a+2} by the reciprocal of \frac{2}{2a^{2}-5a}.

$$\frac{3\left(2a^{2}-5a\right)}{\left(-2-3a+2\right)\times 2}$$

Add -2 and 2 to get 0.

$$\frac{3\left(2a^{2}-5a\right)}{-3a\times 2}$$

Multiply -3 and 2 to get -6.

$$\frac{3\left(2a^{2}-5a\right)}{-6a}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2a^{2}-5a}{-2a}$$

Factor the expressions that are not already factored.

$$\frac{a\left(2a-5\right)}{-2a}$$

Cancel out a in both numerator and denominator.

$$\frac{2a-5}{-2}$$

Multiply both numerator and denominator by -1.

$$\frac{-2a+5}{2}$$

Differentiate w.r.t. a

$$-1$$