Solve a/2a-3-6a/4a^2-9*78

$$\frac { a } { 2 a - 3 } - \frac { 6 a } { 4 a ^ { 2 } - 9 } \cdot 78$$

Evaluate

$$\frac{a\left(2a-465\right)}{4a^{2}-9}$$

Short Solution Steps

Express \frac{6a}{4a^{2}-9}\times 78 as a single fraction.

$$\frac{a}{2a-3}-\frac{6a\times 78}{4a^{2}-9}$$

Multiply 6 and 78 to get 468.

$$\frac{a}{2a-3}-\frac{468a}{4a^{2}-9}$$

Factor 4a^{2}-9.

$$\frac{a}{2a-3}-\frac{468a}{\left(2a-3\right)\left(2a+3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a-3 and \left(2a-3\right)\left(2a+3\right) is \left(2a-3\right)\left(2a+3\right). Multiply \frac{a}{2a-3} times \frac{2a+3}{2a+3}.

$$\frac{a\left(2a+3\right)}{\left(2a-3\right)\left(2a+3\right)}-\frac{468a}{\left(2a-3\right)\left(2a+3\right)}$$

Since \frac{a\left(2a+3\right)}{\left(2a-3\right)\left(2a+3\right)} and \frac{468a}{\left(2a-3\right)\left(2a+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a\left(2a+3\right)-468a}{\left(2a-3\right)\left(2a+3\right)}$$

Do the multiplications in a\left(2a+3\right)-468a.

$$\frac{2a^{2}+3a-468a}{\left(2a-3\right)\left(2a+3\right)}$$

Combine like terms in 2a^{2}+3a-468a.

$$\frac{2a^{2}-465a}{\left(2a-3\right)\left(2a+3\right)}$$

Expand \left(2a-3\right)\left(2a+3\right).

$$\frac{2a^{2}-465a}{4a^{2}-9}$$

Factor

$$\frac{a\left(2a-465\right)}{4a^{2}-9}$$