Solve 4a+3/12a^2-3-1/2a-1-a/6a+3

$$\frac { 4 a + 3 } { 12 a ^ { 2 } - 3 } - \frac { 1 } { 2 a - 1 } - \frac { a } { 6 a + 3 }$$

Evaluate

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

Short Solution Steps

Factor 12a^{2}-3.

$$\frac{4a+3}{3\left(2a-1\right)\left(2a+1\right)}-\frac{1}{2a-1}-\frac{a}{6a+3}$$

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

$$\frac{4a+3}{3\left(2a-1\right)\left(2a+1\right)}-\frac{3\left(2a+1\right)}{3\left(2a-1\right)\left(2a+1\right)}-\frac{a}{6a+3}$$

Since \frac{4a+3}{3\left(2a-1\right)\left(2a+1\right)} and \frac{3\left(2a+1\right)}{3\left(2a-1\right)\left(2a+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4a+3-3\left(2a+1\right)}{3\left(2a-1\right)\left(2a+1\right)}-\frac{a}{6a+3}$$

Do the multiplications in 4a+3-3\left(2a+1\right).

$$\frac{4a+3-6a-3}{3\left(2a-1\right)\left(2a+1\right)}-\frac{a}{6a+3}$$

Combine like terms in 4a+3-6a-3.

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

Factor 6a+3.

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

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

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

Since \frac{-2a}{3\left(2a-1\right)\left(2a+1\right)} and \frac{a\left(2a-1\right)}{3\left(2a-1\right)\left(2a+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -2a-a\left(2a-1\right).

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

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

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

Factor the expressions that are not already factored in \frac{-a-2a^{2}}{3\left(2a-1\right)\left(2a+1\right)}.

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

Extract the negative sign in -1-2a.

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

Cancel out 2a+1 in both numerator and denominator.

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

Expand 3\left(2a-1\right).

$$\frac{-a}{6a-3}$$

Expand

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

Short Solution Steps

Factor 12a^{2}-3.

$$\frac{4a+3}{3\left(2a-1\right)\left(2a+1\right)}-\frac{1}{2a-1}-\frac{a}{6a+3}$$

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

$$\frac{4a+3}{3\left(2a-1\right)\left(2a+1\right)}-\frac{3\left(2a+1\right)}{3\left(2a-1\right)\left(2a+1\right)}-\frac{a}{6a+3}$$

Since \frac{4a+3}{3\left(2a-1\right)\left(2a+1\right)} and \frac{3\left(2a+1\right)}{3\left(2a-1\right)\left(2a+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4a+3-3\left(2a+1\right)}{3\left(2a-1\right)\left(2a+1\right)}-\frac{a}{6a+3}$$

Do the multiplications in 4a+3-3\left(2a+1\right).

$$\frac{4a+3-6a-3}{3\left(2a-1\right)\left(2a+1\right)}-\frac{a}{6a+3}$$

Combine like terms in 4a+3-6a-3.

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

Factor 6a+3.

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

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

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

Since \frac{-2a}{3\left(2a-1\right)\left(2a+1\right)} and \frac{a\left(2a-1\right)}{3\left(2a-1\right)\left(2a+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -2a-a\left(2a-1\right).

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

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

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

Factor the expressions that are not already factored in \frac{-a-2a^{2}}{3\left(2a-1\right)\left(2a+1\right)}.

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

Extract the negative sign in -1-2a.

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

Cancel out 2a+1 in both numerator and denominator.

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

Expand 3\left(2a-1\right).

$$\frac{-a}{6a-3}$$