Solve -16w/3(4w+1)+1/3w(4w+1)-7/w

$$\frac { - 16 w } { 3 ( 4 w + 1 ) } + \frac { 1 } { 3 w ( 4 w + 1 ) } - \frac { 7 } { w }$$

Evaluate

$$-\frac{4}{3}-\frac{20}{3w}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(4w+1\right) and 3w\left(4w+1\right) is 3w\left(4w+1\right). Multiply \frac{-16w}{3\left(4w+1\right)} times \frac{w}{w}.

$$\frac{-16ww}{3w\left(4w+1\right)}+\frac{1}{3w\left(4w+1\right)}-\frac{7}{w}$$

Since \frac{-16ww}{3w\left(4w+1\right)} and \frac{1}{3w\left(4w+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{-16ww+1}{3w\left(4w+1\right)}-\frac{7}{w}$$

Do the multiplications in -16ww+1.

$$\frac{-16w^{2}+1}{3w\left(4w+1\right)}-\frac{7}{w}$$

Factor the expressions that are not already factored in \frac{-16w^{2}+1}{3w\left(4w+1\right)}.

$$\frac{\left(-4w-1\right)\left(4w-1\right)}{3w\left(4w+1\right)}-\frac{7}{w}$$

Extract the negative sign in -1-4w.

$$\frac{-\left(4w-1\right)\left(4w+1\right)}{3w\left(4w+1\right)}-\frac{7}{w}$$

Cancel out 4w+1 in both numerator and denominator.

$$\frac{-\left(4w-1\right)}{3w}-\frac{7}{w}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3w and w is 3w. Multiply \frac{7}{w} times \frac{3}{3}.

$$\frac{-\left(4w-1\right)}{3w}-\frac{7\times 3}{3w}$$

Since \frac{-\left(4w-1\right)}{3w} and \frac{7\times 3}{3w} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\left(4w-1\right)-7\times 3}{3w}$$

Do the multiplications in -\left(4w-1\right)-7\times 3.

$$\frac{-4w+1-21}{3w}$$

Combine like terms in -4w+1-21.

$$\frac{-4w-20}{3w}$$

Expand

$$-\frac{4}{3}-\frac{20}{3w}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(4w+1\right) and 3w\left(4w+1\right) is 3w\left(4w+1\right). Multiply \frac{-16w}{3\left(4w+1\right)} times \frac{w}{w}.

$$\frac{-16ww}{3w\left(4w+1\right)}+\frac{1}{3w\left(4w+1\right)}-\frac{7}{w}$$

Since \frac{-16ww}{3w\left(4w+1\right)} and \frac{1}{3w\left(4w+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{-16ww+1}{3w\left(4w+1\right)}-\frac{7}{w}$$

Do the multiplications in -16ww+1.

$$\frac{-16w^{2}+1}{3w\left(4w+1\right)}-\frac{7}{w}$$

Factor the expressions that are not already factored in \frac{-16w^{2}+1}{3w\left(4w+1\right)}.

$$\frac{\left(-4w-1\right)\left(4w-1\right)}{3w\left(4w+1\right)}-\frac{7}{w}$$

Extract the negative sign in -1-4w.

$$\frac{-\left(4w-1\right)\left(4w+1\right)}{3w\left(4w+1\right)}-\frac{7}{w}$$

Cancel out 4w+1 in both numerator and denominator.

$$\frac{-\left(4w-1\right)}{3w}-\frac{7}{w}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3w and w is 3w. Multiply \frac{7}{w} times \frac{3}{3}.

$$\frac{-\left(4w-1\right)}{3w}-\frac{7\times 3}{3w}$$

Since \frac{-\left(4w-1\right)}{3w} and \frac{7\times 3}{3w} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\left(4w-1\right)-7\times 3}{3w}$$

Do the multiplications in -\left(4w-1\right)-7\times 3.

$$\frac{-4w+1-21}{3w}$$

Combine like terms in -4w+1-21.

$$\frac{-4w-20}{3w}$$