Solve 2x^4/4^2+3*5/2-2x(-2)/(-2^2)+3*5/2

$$\frac { 2 x ^ { 4 } } { 4 ^ { 2 } + 3 } \times \frac { 5 } { 2 } - \frac { 2 x ( - 2 ) } { ( - 2 ^ { 2 } ) + 3 } \times \frac { 5 } { 2 }$$

Evaluate

$$\frac{5x^{4}}{19}-10x$$

Short Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{2x^{4}}{16+3}\times \frac{5}{2}-\frac{2x\left(-2\right)}{-2^{2}+3}\times \frac{5}{2}$$

Add 16 and 3 to get 19.

$$\frac{2x^{4}}{19}\times \frac{5}{2}-\frac{2x\left(-2\right)}{-2^{2}+3}\times \frac{5}{2}$$

Multiply \frac{2x^{4}}{19} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x^{4}\times 5}{19\times 2}-\frac{2x\left(-2\right)}{-2^{2}+3}\times \frac{5}{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5x^{4}}{19}-\frac{2x\left(-2\right)}{-2^{2}+3}\times \frac{5}{2}$$

Multiply 2 and -2 to get -4.

$$\frac{5x^{4}}{19}-\frac{-4x}{-2^{2}+3}\times \frac{5}{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{5x^{4}}{19}-\frac{-4x}{-4+3}\times \frac{5}{2}$$

Add -4 and 3 to get -1.

$$\frac{5x^{4}}{19}-\frac{-4x}{-1}\times \frac{5}{2}$$

Anything divided by -1 gives its opposite.

$$\frac{5x^{4}}{19}-4x\times \frac{5}{2}$$

Multiply 4 and \frac{5}{2} to get 10.

$$\frac{5x^{4}}{19}-10x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -10x times \frac{19}{19}.

$$\frac{5x^{4}}{19}+\frac{19\left(-10\right)x}{19}$$

Since \frac{5x^{4}}{19} and \frac{19\left(-10\right)x}{19} have the same denominator, add them by adding their numerators.

$$\frac{5x^{4}+19\left(-10\right)x}{19}$$

Do the multiplications in 5x^{4}+19\left(-10\right)x.

$$\frac{5x^{4}-190x}{19}$$

Factor

$$\frac{5x\left(x^{3}-38\right)}{19}$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$factor(\frac{2x^{4}}{16+3}\times \frac{5}{2}-\frac{2x\left(-2\right)}{-2^{2}+3}\times \frac{5}{2})$$

Add 16 and 3 to get 19.

$$factor(\frac{2x^{4}}{19}\times \frac{5}{2}-\frac{2x\left(-2\right)}{-2^{2}+3}\times \frac{5}{2})$$

Multiply \frac{2x^{4}}{19} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$factor(\frac{2x^{4}\times 5}{19\times 2}-\frac{2x\left(-2\right)}{-2^{2}+3}\times \frac{5}{2})$$

Cancel out 2 in both numerator and denominator.

$$factor(\frac{5x^{4}}{19}-\frac{2x\left(-2\right)}{-2^{2}+3}\times \frac{5}{2})$$

Multiply 2 and -2 to get -4.

$$factor(\frac{5x^{4}}{19}-\frac{-4x}{-2^{2}+3}\times \frac{5}{2})$$

Calculate 2 to the power of 2 and get 4.

$$factor(\frac{5x^{4}}{19}-\frac{-4x}{-4+3}\times \frac{5}{2})$$

Add -4 and 3 to get -1.

$$factor(\frac{5x^{4}}{19}-\frac{-4x}{-1}\times \frac{5}{2})$$

Anything divided by -1 gives its opposite.

$$factor(\frac{5x^{4}}{19}-4x\times \frac{5}{2})$$

Multiply 4 and \frac{5}{2} to get 10.

$$factor(\frac{5x^{4}}{19}-10x)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -10x times \frac{19}{19}.

$$factor(\frac{5x^{4}}{19}+\frac{19\left(-10\right)x}{19})$$

Since \frac{5x^{4}}{19} and \frac{19\left(-10\right)x}{19} have the same denominator, add them by adding their numerators.

$$factor(\frac{5x^{4}+19\left(-10\right)x}{19})$$

Do the multiplications in 5x^{4}+19\left(-10\right)x.

$$factor(\frac{5x^{4}-190x}{19})$$

Consider 5x^{4}-190x. Factor out 5.

$$5\left(x^{4}-38x\right)$$

Consider x^{4}-38x. Factor out x.

$$x\left(x^{3}-38\right)$$

Rewrite the complete factored expression. Simplify. Polynomial x^{3}-38 is not factored since it does not have any rational roots.

$$\frac{5x\left(x^{3}-38\right)}{19}$$