Solve {l}{7/4b^2+6a/b}{-1}

$$\left. \begin{array} { l } { \frac { 7 } { 4 b ^ { 2 } } + \frac { 6 a } { b } } \\ { - 1 } \end{array} \right.$$

Evaluate

$$\frac{6a}{b}-1+\frac{7}{4b^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4b^{2} and b is 4b^{2}. Multiply \frac{6a}{b} times \frac{4b}{4b}.

$$\frac{7}{4b^{2}}+\frac{6a\times 4b}{4b^{2}}-1$$

Since \frac{7}{4b^{2}} and \frac{6a\times 4b}{4b^{2}} have the same denominator, add them by adding their numerators.

$$\frac{7+6a\times 4b}{4b^{2}}-1$$

Do the multiplications in 7+6a\times 4b.

$$\frac{7+24ab}{4b^{2}}-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4b^{2}}{4b^{2}}.

$$\frac{7+24ab}{4b^{2}}-\frac{4b^{2}}{4b^{2}}$$

Since \frac{7+24ab}{4b^{2}} and \frac{4b^{2}}{4b^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7+24ab-4b^{2}}{4b^{2}}$$

Factor

$$\frac{24ab-4b^{2}+7}{4b^{2}}$$