Solve 22w+11/8w^2-6w-3/2wquad112w/2

$$\frac { 22 w + 11 } { 8 w ^ { 2 } - 6 w } - \frac { 3 } { 2 w } \quad \frac { 112 w } { 2 }$$

Evaluate

$$\frac{11+526w-672w^{2}}{2w\left(4w-3\right)}$$

Short Solution Steps

Divide 112w by 2 to get 56w.

$$\frac{22w+11}{8w^{2}-6w}-\frac{3}{2w}\times 56w$$

Express \frac{3}{2w}\times 56 as a single fraction.

$$\frac{22w+11}{8w^{2}-6w}-\frac{3\times 56}{2w}w$$

Cancel out 2 in both numerator and denominator.

$$\frac{22w+11}{8w^{2}-6w}-\frac{3\times 28}{w}w$$

Cancel out w and w.

$$\frac{22w+11}{8w^{2}-6w}-3\times 28$$

Factor 8w^{2}-6w.

$$\frac{22w+11}{2w\left(4w-3\right)}-3\times 28$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3\times 28 times \frac{2w\left(4w-3\right)}{2w\left(4w-3\right)}.

$$\frac{22w+11}{2w\left(4w-3\right)}-\frac{3\times 28\times 2w\left(4w-3\right)}{2w\left(4w-3\right)}$$

Since \frac{22w+11}{2w\left(4w-3\right)} and \frac{3\times 28\times 2w\left(4w-3\right)}{2w\left(4w-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22w+11-3\times 28\times 2w\left(4w-3\right)}{2w\left(4w-3\right)}$$

Do the multiplications in 22w+11-3\times 28\times 2w\left(4w-3\right).

$$\frac{22w+11-672w^{2}+504w}{2w\left(4w-3\right)}$$

Combine like terms in 22w+11-672w^{2}+504w.

$$\frac{526w+11-672w^{2}}{2w\left(4w-3\right)}$$

Factor the expressions that are not already factored in \frac{526w+11-672w^{2}}{2w\left(4w-3\right)}.

$$\frac{-672\left(w-\left(-\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)\left(w-\left(\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)}{2w\left(4w-3\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-336\left(w-\left(-\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)\left(w-\left(\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)}{w\left(4w-3\right)}$$

Expand w\left(4w-3\right).

$$\frac{-336\left(w-\left(-\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)\left(w-\left(\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)}{4w^{2}-3w}$$

To find the opposite of -\frac{1}{672}\sqrt{76561}+\frac{263}{672}, find the opposite of each term.

$$\frac{-336\left(w+\frac{1}{672}\sqrt{76561}-\frac{263}{672}\right)\left(w-\left(\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)}{4w^{2}-3w}$$

To find the opposite of \frac{1}{672}\sqrt{76561}+\frac{263}{672}, find the opposite of each term.

$$\frac{-336\left(w+\frac{1}{672}\sqrt{76561}-\frac{263}{672}\right)\left(w-\frac{1}{672}\sqrt{76561}-\frac{263}{672}\right)}{4w^{2}-3w}$$

Use the distributive property to multiply -336 by w+\frac{1}{672}\sqrt{76561}-\frac{263}{672}.

$$\frac{\left(-336w-\frac{1}{2}\sqrt{76561}+\frac{263}{2}\right)\left(w-\frac{1}{672}\sqrt{76561}-\frac{263}{672}\right)}{4w^{2}-3w}$$

Use the distributive property to multiply -336w-\frac{1}{2}\sqrt{76561}+\frac{263}{2} by w-\frac{1}{672}\sqrt{76561}-\frac{263}{672} and combine like terms.

$$\frac{-336w^{2}+263w+\frac{1}{1344}\left(\sqrt{76561}\right)^{2}-\frac{69169}{1344}}{4w^{2}-3w}$$

The square of \sqrt{76561} is 76561.

$$\frac{-336w^{2}+263w+\frac{1}{1344}\times 76561-\frac{69169}{1344}}{4w^{2}-3w}$$

Multiply \frac{1}{1344} and 76561 to get \frac{76561}{1344}.

$$\frac{-336w^{2}+263w+\frac{76561}{1344}-\frac{69169}{1344}}{4w^{2}-3w}$$

Subtract \frac{69169}{1344} from \frac{76561}{1344} to get \frac{11}{2}.

$$\frac{-336w^{2}+263w+\frac{11}{2}}{4w^{2}-3w}$$

Expand

$$-\frac{672w^{2}-526w-11}{2\left(4w^{2}-3w\right)}$$

Short Solution Steps

Divide 112w by 2 to get 56w.

$$\frac{22w+11}{8w^{2}-6w}-\frac{3}{2w}\times 56w$$

Express \frac{3}{2w}\times 56 as a single fraction.

$$\frac{22w+11}{8w^{2}-6w}-\frac{3\times 56}{2w}w$$

Cancel out 2 in both numerator and denominator.

$$\frac{22w+11}{8w^{2}-6w}-\frac{3\times 28}{w}w$$

Cancel out w and w.

$$\frac{22w+11}{8w^{2}-6w}-3\times 28$$

Factor 8w^{2}-6w.

$$\frac{22w+11}{2w\left(4w-3\right)}-3\times 28$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3\times 28 times \frac{2w\left(4w-3\right)}{2w\left(4w-3\right)}.

$$\frac{22w+11}{2w\left(4w-3\right)}-\frac{3\times 28\times 2w\left(4w-3\right)}{2w\left(4w-3\right)}$$

Since \frac{22w+11}{2w\left(4w-3\right)} and \frac{3\times 28\times 2w\left(4w-3\right)}{2w\left(4w-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22w+11-3\times 28\times 2w\left(4w-3\right)}{2w\left(4w-3\right)}$$

Do the multiplications in 22w+11-3\times 28\times 2w\left(4w-3\right).

$$\frac{22w+11-672w^{2}+504w}{2w\left(4w-3\right)}$$

Combine like terms in 22w+11-672w^{2}+504w.

$$\frac{526w+11-672w^{2}}{2w\left(4w-3\right)}$$

Factor the expressions that are not already factored in \frac{526w+11-672w^{2}}{2w\left(4w-3\right)}.

$$\frac{-672\left(w-\left(-\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)\left(w-\left(\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)}{2w\left(4w-3\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-336\left(w-\left(-\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)\left(w-\left(\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)}{w\left(4w-3\right)}$$

Expand w\left(4w-3\right).

$$\frac{-336\left(w-\left(-\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)\left(w-\left(\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)}{4w^{2}-3w}$$

To find the opposite of -\frac{1}{672}\sqrt{76561}+\frac{263}{672}, find the opposite of each term.

$$\frac{-336\left(w+\frac{1}{672}\sqrt{76561}-\frac{263}{672}\right)\left(w-\left(\frac{1}{672}\sqrt{76561}+\frac{263}{672}\right)\right)}{4w^{2}-3w}$$

To find the opposite of \frac{1}{672}\sqrt{76561}+\frac{263}{672}, find the opposite of each term.

$$\frac{-336\left(w+\frac{1}{672}\sqrt{76561}-\frac{263}{672}\right)\left(w-\frac{1}{672}\sqrt{76561}-\frac{263}{672}\right)}{4w^{2}-3w}$$

Use the distributive property to multiply -336 by w+\frac{1}{672}\sqrt{76561}-\frac{263}{672}.

$$\frac{\left(-336w-\frac{1}{2}\sqrt{76561}+\frac{263}{2}\right)\left(w-\frac{1}{672}\sqrt{76561}-\frac{263}{672}\right)}{4w^{2}-3w}$$

Use the distributive property to multiply -336w-\frac{1}{2}\sqrt{76561}+\frac{263}{2} by w-\frac{1}{672}\sqrt{76561}-\frac{263}{672} and combine like terms.

$$\frac{-336w^{2}+263w+\frac{1}{1344}\left(\sqrt{76561}\right)^{2}-\frac{69169}{1344}}{4w^{2}-3w}$$

The square of \sqrt{76561} is 76561.

$$\frac{-336w^{2}+263w+\frac{1}{1344}\times 76561-\frac{69169}{1344}}{4w^{2}-3w}$$

Multiply \frac{1}{1344} and 76561 to get \frac{76561}{1344}.

$$\frac{-336w^{2}+263w+\frac{76561}{1344}-\frac{69169}{1344}}{4w^{2}-3w}$$

Subtract \frac{69169}{1344} from \frac{76561}{1344} to get \frac{11}{2}.

$$\frac{-336w^{2}+263w+\frac{11}{2}}{4w^{2}-3w}$$