Solve 2b/3a+a/6b-1+4b^2/6ab=

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

Evaluate

$$\frac{a^{2}-1}{6ab}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 6b is 6ab. Multiply \frac{2b}{3a} times \frac{2b}{2b}. Multiply \frac{a}{6b} times \frac{a}{a}.

$$\frac{2b\times 2b}{6ab}+\frac{aa}{6ab}-\frac{1+4b^{2}}{6ab}$$

Since \frac{2b\times 2b}{6ab} and \frac{aa}{6ab} have the same denominator, add them by adding their numerators.

$$\frac{2b\times 2b+aa}{6ab}-\frac{1+4b^{2}}{6ab}$$

Do the multiplications in 2b\times 2b+aa.

$$\frac{4b^{2}+a^{2}}{6ab}-\frac{1+4b^{2}}{6ab}$$

Since \frac{4b^{2}+a^{2}}{6ab} and \frac{1+4b^{2}}{6ab} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4b^{2}+a^{2}-\left(1+4b^{2}\right).

$$\frac{4b^{2}+a^{2}-1-4b^{2}}{6ab}$$

Combine like terms in 4b^{2}+a^{2}-1-4b^{2}.

$$\frac{a^{2}-1}{6ab}$$

Expand

$$\frac{a^{2}-1}{6ab}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 6b is 6ab. Multiply \frac{2b}{3a} times \frac{2b}{2b}. Multiply \frac{a}{6b} times \frac{a}{a}.

$$\frac{2b\times 2b}{6ab}+\frac{aa}{6ab}-\frac{1+4b^{2}}{6ab}$$

Since \frac{2b\times 2b}{6ab} and \frac{aa}{6ab} have the same denominator, add them by adding their numerators.

$$\frac{2b\times 2b+aa}{6ab}-\frac{1+4b^{2}}{6ab}$$

Do the multiplications in 2b\times 2b+aa.

$$\frac{4b^{2}+a^{2}}{6ab}-\frac{1+4b^{2}}{6ab}$$

Since \frac{4b^{2}+a^{2}}{6ab} and \frac{1+4b^{2}}{6ab} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4b^{2}+a^{2}-\left(1+4b^{2}\right).

$$\frac{4b^{2}+a^{2}-1-4b^{2}}{6ab}$$

Combine like terms in 4b^{2}+a^{2}-1-4b^{2}.

$$\frac{a^{2}-1}{6ab}$$