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

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

Evaluate

$$\frac{100x}{19}-5$$

Short Solution Steps

Calculate x to the power of 1 and get x.

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

Calculate 4 to the power of 2 and get 16.

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

Add 16 and 3 to get 19.

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

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

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

Cancel out 2 in both numerator and denominator.

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

Calculate 2 to the power of 2 and get 4.

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

Add -4 and 3 to get -1.

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

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

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

Use the distributive property to multiply -2x+2 by \frac{5}{2}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 5x-5 times \frac{19}{19}.

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

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

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

Do the multiplications in 5x+19\left(5x-5\right).

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

Combine like terms in 5x+95x-95.

$$\frac{100x-95}{19}$$

Expand

$$\frac{100x}{19}-5$$

Short Solution Steps

Calculate x to the power of 1 and get x.

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

Calculate 4 to the power of 2 and get 16.

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

Add 16 and 3 to get 19.

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

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

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

Cancel out 2 in both numerator and denominator.

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

Calculate 2 to the power of 2 and get 4.

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

Add -4 and 3 to get -1.

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

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

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

Use the distributive property to multiply -2x+2 by \frac{5}{2}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 5x-5 times \frac{19}{19}.

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

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

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

Do the multiplications in 5x+19\left(5x-5\right).

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

Combine like terms in 5x+95x-95.

$$\frac{100x-95}{19}$$