Solve 1/4-6/3+b^2/9

$$\frac { 1 } { 4 } - \frac { 6 } { 3 } + \frac { b ^ { 2 } } { 9 }$$

Evaluate

$$\frac{b^{2}}{9}-\frac{7}{4}$$

Short Solution Steps

Divide 6 by 3 to get 2.

$$\frac{1}{4}-2+\frac{b^{2}}{9}$$

Subtract 2 from \frac{1}{4} to get -\frac{7}{4}.

$$-\frac{7}{4}+\frac{b^{2}}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 9 is 36. Multiply -\frac{7}{4} times \frac{9}{9}. Multiply \frac{b^{2}}{9} times \frac{4}{4}.

$$-\frac{7\times 9}{36}+\frac{4b^{2}}{36}$$

Since -\frac{7\times 9}{36} and \frac{4b^{2}}{36} have the same denominator, add them by adding their numerators.

$$\frac{-7\times 9+4b^{2}}{36}$$

Do the multiplications in -7\times 9+4b^{2}.

$$\frac{-63+4b^{2}}{36}$$

Factor

$$\frac{4b^{2}-63}{36}$$

Solution Steps

Factor out \frac{1}{36}. Polynomial 4b^{2}-63 is not factored since it does not have any rational roots.

$$\frac{-63+4b^{2}}{36}$$