Solve (((7/6x)(3/5x^2))div(-x^2)+x)(3x-(-4x))-1/2x^2

$$((( \frac{ 7 }{ 6 } x)( \frac{ 3 }{ 5 } { x }^{ 2 } )) \div (- { x }^{ 2 } )+x)(3x-(-4x))- \frac{ 1 }{ 2 } { x }^{ 2 }$$

Evaluate

$$\frac{8x^{2}}{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(\frac{\frac{7}{6}x^{3}\times \frac{3}{5}}{-x^{2}}+x\right)\left(3x-\left(-4x\right)\right)-\frac{1}{2}x^{2}$$

Multiply \frac{7}{6} and \frac{3}{5} to get \frac{7}{10}.

$$\left(\frac{\frac{7}{10}x^{3}}{-x^{2}}+x\right)\left(3x-\left(-4x\right)\right)-\frac{1}{2}x^{2}$$

The opposite of -4x is 4x.

$$\left(\frac{\frac{7}{10}x^{3}}{-x^{2}}+x\right)\left(3x+4x\right)-\frac{1}{2}x^{2}$$

Combine 3x and 4x to get 7x.

$$\left(\frac{\frac{7}{10}x^{3}}{-x^{2}}+x\right)\times 7x-\frac{1}{2}x^{2}$$

Use the distributive property to multiply \frac{\frac{7}{10}x^{3}}{-x^{2}}+x by 7.

$$\left(7\times \frac{\frac{7}{10}x^{3}}{-x^{2}}+7x\right)x-\frac{1}{2}x^{2}$$

Use the distributive property to multiply 7\times \frac{\frac{7}{10}x^{3}}{-x^{2}}+7x by x.

$$7\times \frac{\frac{7}{10}x^{3}}{-x^{2}}x+7x^{2}-\frac{1}{2}x^{2}$$

Combine 7x^{2} and -\frac{1}{2}x^{2} to get \frac{13}{2}x^{2}.

$$7\times \frac{\frac{7}{10}x^{3}}{-x^{2}}x+\frac{13}{2}x^{2}$$

Cancel out x^{2} in both numerator and denominator.

$$7\times \frac{\frac{7}{10}x}{-1}x+\frac{13}{2}x^{2}$$

Anything divided by -1 gives its opposite.

$$7\left(-\frac{7}{10}\right)xx+\frac{13}{2}x^{2}$$

Multiply 7 and -\frac{7}{10} to get -\frac{49}{10}.

$$-\frac{49}{10}xx+\frac{13}{2}x^{2}$$

Multiply x and x to get x^{2}.

$$-\frac{49}{10}x^{2}+\frac{13}{2}x^{2}$$

Combine -\frac{49}{10}x^{2} and \frac{13}{2}x^{2} to get \frac{8}{5}x^{2}.

$$\frac{8}{5}x^{2}$$

Expand

$$\frac{8x^{2}}{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(\frac{\frac{7}{6}x^{3}\times \frac{3}{5}}{-x^{2}}+x\right)\left(3x-\left(-4x\right)\right)-\frac{1}{2}x^{2}$$

Multiply \frac{7}{6} and \frac{3}{5} to get \frac{7}{10}.

$$\left(\frac{\frac{7}{10}x^{3}}{-x^{2}}+x\right)\left(3x-\left(-4x\right)\right)-\frac{1}{2}x^{2}$$

The opposite of -4x is 4x.

$$\left(\frac{\frac{7}{10}x^{3}}{-x^{2}}+x\right)\left(3x+4x\right)-\frac{1}{2}x^{2}$$

Combine 3x and 4x to get 7x.

$$\left(\frac{\frac{7}{10}x^{3}}{-x^{2}}+x\right)\times 7x-\frac{1}{2}x^{2}$$

Use the distributive property to multiply \frac{\frac{7}{10}x^{3}}{-x^{2}}+x by 7.

$$\left(7\times \frac{\frac{7}{10}x^{3}}{-x^{2}}+7x\right)x-\frac{1}{2}x^{2}$$

Use the distributive property to multiply 7\times \frac{\frac{7}{10}x^{3}}{-x^{2}}+7x by x.

$$7\times \frac{\frac{7}{10}x^{3}}{-x^{2}}x+7x^{2}-\frac{1}{2}x^{2}$$

Combine 7x^{2} and -\frac{1}{2}x^{2} to get \frac{13}{2}x^{2}.

$$7\times \frac{\frac{7}{10}x^{3}}{-x^{2}}x+\frac{13}{2}x^{2}$$

Cancel out x^{2} in both numerator and denominator.

$$7\times \frac{\frac{7}{10}x}{-1}x+\frac{13}{2}x^{2}$$

Anything divided by -1 gives its opposite.

$$7\left(-\frac{7}{10}\right)xx+\frac{13}{2}x^{2}$$

Multiply 7 and -\frac{7}{10} to get -\frac{49}{10}.

$$-\frac{49}{10}xx+\frac{13}{2}x^{2}$$

Multiply x and x to get x^{2}.

$$-\frac{49}{10}x^{2}+\frac{13}{2}x^{2}$$

Combine -\frac{49}{10}x^{2} and \frac{13}{2}x^{2} to get \frac{8}{5}x^{2}.

$$\frac{8}{5}x^{2}$$