Solve 2*4/4^2+35/2-2x-2/-2^2+35/2

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

Evaluate

$$5x-\frac{75}{19}$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{8}{4^{2}+3}\times \frac{5}{2}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{8}{16+3}\times \frac{5}{2}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Add 16 and 3 to get 19.

$$\frac{8}{19}\times \frac{5}{2}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Multiply \frac{8}{19} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 5}{19\times 2}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Do the multiplications in the fraction \frac{8\times 5}{19\times 2}.

$$\frac{40}{38}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Reduce the fraction \frac{40}{38} to lowest terms by extracting and canceling out 2.

$$\frac{20}{19}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{20}{19}-\frac{2x-2}{-4+3}\times \frac{5}{2}$$

Add -4 and 3 to get -1.

$$\frac{20}{19}-\frac{2x-2}{-1}\times \frac{5}{2}$$

Anything divided by -1 gives its opposite. To find the opposite of 2x-2, find the opposite of each term.

$$\frac{20}{19}-\left(-2x-\left(-2\right)\right)\times \frac{5}{2}$$

Use the distributive property to multiply -2x-\left(-2\right) by \frac{5}{2}.

$$\frac{20}{19}-\left(-2x\times \frac{5}{2}+\left(-\left(-2\right)\right)\times \frac{5}{2}\right)$$

Multiply -2 times \frac{5}{2}.

$$\frac{20}{19}-\left(-5x+\left(-\left(-2\right)\right)\times \frac{5}{2}\right)$$

The opposite of -2 is 2.

$$\frac{20}{19}-\left(-5x+2\times \frac{5}{2}\right)$$

Cancel out 2 and 2.

$$\frac{20}{19}-\left(-5x+5\right)$$

To find the opposite of -5x+5, find the opposite of each term.

$$\frac{20}{19}-\left(-5x\right)-5$$

The opposite of -5x is 5x.

$$\frac{20}{19}+5x-5$$

Convert 5 to fraction \frac{95}{19}.

$$\frac{20}{19}+5x-\frac{95}{19}$$

Since \frac{20}{19} and \frac{95}{19} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-95}{19}+5x$$

Subtract 95 from 20 to get -75.

$$-\frac{75}{19}+5x$$

Expand

$$5x-\frac{75}{19}$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{8}{4^{2}+3}\times \frac{5}{2}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{8}{16+3}\times \frac{5}{2}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Add 16 and 3 to get 19.

$$\frac{8}{19}\times \frac{5}{2}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Multiply \frac{8}{19} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 5}{19\times 2}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Do the multiplications in the fraction \frac{8\times 5}{19\times 2}.

$$\frac{40}{38}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Reduce the fraction \frac{40}{38} to lowest terms by extracting and canceling out 2.

$$\frac{20}{19}-\frac{2x-2}{-2^{2}+3}\times \frac{5}{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{20}{19}-\frac{2x-2}{-4+3}\times \frac{5}{2}$$

Add -4 and 3 to get -1.

$$\frac{20}{19}-\frac{2x-2}{-1}\times \frac{5}{2}$$

Anything divided by -1 gives its opposite. To find the opposite of 2x-2, find the opposite of each term.

$$\frac{20}{19}-\left(-2x-\left(-2\right)\right)\times \frac{5}{2}$$

Use the distributive property to multiply -2x-\left(-2\right) by \frac{5}{2}.

$$\frac{20}{19}-\left(-2x\times \frac{5}{2}+\left(-\left(-2\right)\right)\times \frac{5}{2}\right)$$

Multiply -2 times \frac{5}{2}.

$$\frac{20}{19}-\left(-5x+\left(-\left(-2\right)\right)\times \frac{5}{2}\right)$$

The opposite of -2 is 2.

$$\frac{20}{19}-\left(-5x+2\times \frac{5}{2}\right)$$

Cancel out 2 and 2.

$$\frac{20}{19}-\left(-5x+5\right)$$

To find the opposite of -5x+5, find the opposite of each term.

$$\frac{20}{19}-\left(-5x\right)-5$$

The opposite of -5x is 5x.

$$\frac{20}{19}+5x-5$$

Convert 5 to fraction \frac{95}{19}.

$$\frac{20}{19}+5x-\frac{95}{19}$$

Since \frac{20}{19} and \frac{95}{19} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-95}{19}+5x$$

Subtract 95 from 20 to get -75.

$$-\frac{75}{19}+5x$$