Solve 3/9+2/5a-3+1-8aa/25a^2-a=

$$\frac { 3 } { 9 } + \frac { 2 } { 5 a - 3 } + \frac { 1 - 8 a a } { 25 a ^ { 2 } - a } =$$

Evaluate

$$\frac{5a^{3}+142a^{2}+12a-9}{3a\left(5a-3\right)\left(25a-1\right)}$$

Short Solution Steps

Multiply a and a to get a^{2}.

$$\frac{3}{9}+\frac{2}{5a-3}+\frac{1-8a^{2}}{25a^{2}-a}$$

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

$$\frac{1}{3}+\frac{2}{5a-3}+\frac{1-8a^{2}}{25a^{2}-a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5a-3 is 3\left(5a-3\right). Multiply \frac{1}{3} times \frac{5a-3}{5a-3}. Multiply \frac{2}{5a-3} times \frac{3}{3}.

$$\frac{5a-3}{3\left(5a-3\right)}+\frac{2\times 3}{3\left(5a-3\right)}+\frac{1-8a^{2}}{25a^{2}-a}$$

Since \frac{5a-3}{3\left(5a-3\right)} and \frac{2\times 3}{3\left(5a-3\right)} have the same denominator, add them by adding their numerators.

$$\frac{5a-3+2\times 3}{3\left(5a-3\right)}+\frac{1-8a^{2}}{25a^{2}-a}$$

Do the multiplications in 5a-3+2\times 3.

$$\frac{5a-3+6}{3\left(5a-3\right)}+\frac{1-8a^{2}}{25a^{2}-a}$$

Combine like terms in 5a-3+6.

$$\frac{5a+3}{3\left(5a-3\right)}+\frac{1-8a^{2}}{25a^{2}-a}$$

Factor 25a^{2}-a.

$$\frac{5a+3}{3\left(5a-3\right)}+\frac{1-8a^{2}}{a\left(25a-1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(5a-3\right) and a\left(25a-1\right) is 3a\left(5a-3\right)\left(25a-1\right). Multiply \frac{5a+3}{3\left(5a-3\right)} times \frac{a\left(25a-1\right)}{a\left(25a-1\right)}. Multiply \frac{1-8a^{2}}{a\left(25a-1\right)} times \frac{3\left(5a-3\right)}{3\left(5a-3\right)}.

$$\frac{\left(5a+3\right)a\left(25a-1\right)}{3a\left(5a-3\right)\left(25a-1\right)}+\frac{\left(1-8a^{2}\right)\times 3\left(5a-3\right)}{3a\left(5a-3\right)\left(25a-1\right)}$$

Since \frac{\left(5a+3\right)a\left(25a-1\right)}{3a\left(5a-3\right)\left(25a-1\right)} and \frac{\left(1-8a^{2}\right)\times 3\left(5a-3\right)}{3a\left(5a-3\right)\left(25a-1\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(5a+3\right)a\left(25a-1\right)+\left(1-8a^{2}\right)\times 3\left(5a-3\right)}{3a\left(5a-3\right)\left(25a-1\right)}$$

Do the multiplications in \left(5a+3\right)a\left(25a-1\right)+\left(1-8a^{2}\right)\times 3\left(5a-3\right).

$$\frac{125a^{3}-5a^{2}+75a^{2}-3a+15a-9-120a^{3}+72a^{2}}{3a\left(5a-3\right)\left(25a-1\right)}$$

Combine like terms in 125a^{3}-5a^{2}+75a^{2}-3a+15a-9-120a^{3}+72a^{2}.

$$\frac{5a^{3}+142a^{2}+12a-9}{3a\left(5a-3\right)\left(25a-1\right)}$$

Expand 3a\left(5a-3\right)\left(25a-1\right).

$$\frac{5a^{3}+142a^{2}+12a-9}{375a^{3}-240a^{2}+9a}$$

Expand

$$\frac{5a^{3}+142a^{2}+12a-9}{3\left(5a-3\right)\left(25a^{2}-a\right)}$$

Short Solution Steps

Multiply a and a to get a^{2}.

$$\frac{3}{9}+\frac{2}{5a-3}+\frac{1-8a^{2}}{25a^{2}-a}$$

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

$$\frac{1}{3}+\frac{2}{5a-3}+\frac{1-8a^{2}}{25a^{2}-a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5a-3 is 3\left(5a-3\right). Multiply \frac{1}{3} times \frac{5a-3}{5a-3}. Multiply \frac{2}{5a-3} times \frac{3}{3}.

$$\frac{5a-3}{3\left(5a-3\right)}+\frac{2\times 3}{3\left(5a-3\right)}+\frac{1-8a^{2}}{25a^{2}-a}$$

Since \frac{5a-3}{3\left(5a-3\right)} and \frac{2\times 3}{3\left(5a-3\right)} have the same denominator, add them by adding their numerators.

$$\frac{5a-3+2\times 3}{3\left(5a-3\right)}+\frac{1-8a^{2}}{25a^{2}-a}$$

Do the multiplications in 5a-3+2\times 3.

$$\frac{5a-3+6}{3\left(5a-3\right)}+\frac{1-8a^{2}}{25a^{2}-a}$$

Combine like terms in 5a-3+6.

$$\frac{5a+3}{3\left(5a-3\right)}+\frac{1-8a^{2}}{25a^{2}-a}$$

Factor 25a^{2}-a.

$$\frac{5a+3}{3\left(5a-3\right)}+\frac{1-8a^{2}}{a\left(25a-1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(5a-3\right) and a\left(25a-1\right) is 3a\left(5a-3\right)\left(25a-1\right). Multiply \frac{5a+3}{3\left(5a-3\right)} times \frac{a\left(25a-1\right)}{a\left(25a-1\right)}. Multiply \frac{1-8a^{2}}{a\left(25a-1\right)} times \frac{3\left(5a-3\right)}{3\left(5a-3\right)}.

$$\frac{\left(5a+3\right)a\left(25a-1\right)}{3a\left(5a-3\right)\left(25a-1\right)}+\frac{\left(1-8a^{2}\right)\times 3\left(5a-3\right)}{3a\left(5a-3\right)\left(25a-1\right)}$$

Since \frac{\left(5a+3\right)a\left(25a-1\right)}{3a\left(5a-3\right)\left(25a-1\right)} and \frac{\left(1-8a^{2}\right)\times 3\left(5a-3\right)}{3a\left(5a-3\right)\left(25a-1\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(5a+3\right)a\left(25a-1\right)+\left(1-8a^{2}\right)\times 3\left(5a-3\right)}{3a\left(5a-3\right)\left(25a-1\right)}$$

Do the multiplications in \left(5a+3\right)a\left(25a-1\right)+\left(1-8a^{2}\right)\times 3\left(5a-3\right).

$$\frac{125a^{3}-5a^{2}+75a^{2}-3a+15a-9-120a^{3}+72a^{2}}{3a\left(5a-3\right)\left(25a-1\right)}$$

Combine like terms in 125a^{3}-5a^{2}+75a^{2}-3a+15a-9-120a^{3}+72a^{2}.

$$\frac{5a^{3}+142a^{2}+12a-9}{3a\left(5a-3\right)\left(25a-1\right)}$$

Expand 3a\left(5a-3\right)\left(25a-1\right).

$$\frac{5a^{3}+142a^{2}+12a-9}{375a^{3}-240a^{2}+9a}$$