Solve 2x/x+5-x/x-3*x^2/x-3-(x+1)^2/x+3

$$\frac { 2 x } { x } + 5 - \frac { x } { x - 3 } \times \frac { x ^ { 2 } } { x - 3 } - \frac { ( x + 1 ) ^ { 2 } } { x + 3 }$$

Evaluate

$$\frac{180-75x-19x^{2}+8x^{3}-2x^{4}}{\left(x+3\right)\left(x-3\right)^{2}}$$

Short Solution Steps

Cancel out x in both numerator and denominator.

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

Add 2 and 5 to get 7.

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

Multiply \frac{x}{x-3} times \frac{x^{2}}{x-3} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply x-3 and x-3 to get \left(x-3\right)^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{\left(x-3\right)^{2}}{\left(x-3\right)^{2}}.

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

Since \frac{7\left(x-3\right)^{2}}{\left(x-3\right)^{2}} and \frac{x^{3}}{\left(x-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 7\left(x-3\right)^{2}-x^{3}.

$$\frac{7x^{2}-42x+63-x^{3}}{\left(x-3\right)^{2}}-\frac{\left(x+1\right)^{2}}{x+3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)^{2} and x+3 is \left(x+3\right)\left(x-3\right)^{2}. Multiply \frac{7x^{2}-42x+63-x^{3}}{\left(x-3\right)^{2}} times \frac{x+3}{x+3}. Multiply \frac{\left(x+1\right)^{2}}{x+3} times \frac{\left(x-3\right)^{2}}{\left(x-3\right)^{2}}.

$$\frac{\left(7x^{2}-42x+63-x^{3}\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)^{2}}-\frac{\left(x+1\right)^{2}\left(x-3\right)^{2}}{\left(x+3\right)\left(x-3\right)^{2}}$$

Since \frac{\left(7x^{2}-42x+63-x^{3}\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)^{2}} and \frac{\left(x+1\right)^{2}\left(x-3\right)^{2}}{\left(x+3\right)\left(x-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(7x^{2}-42x+63-x^{3}\right)\left(x+3\right)-\left(x+1\right)^{2}\left(x-3\right)^{2}}{\left(x+3\right)\left(x-3\right)^{2}}$$

Do the multiplications in \left(7x^{2}-42x+63-x^{3}\right)\left(x+3\right)-\left(x+1\right)^{2}\left(x-3\right)^{2}.

$$\frac{7x^{3}+21x^{2}-42x^{2}-126x+63x+189-x^{4}-3x^{3}-x^{4}+6x^{3}-9x^{2}-2x^{3}+12x^{2}-18x-x^{2}+6x-9}{\left(x+3\right)\left(x-3\right)^{2}}$$

Combine like terms in 7x^{3}+21x^{2}-42x^{2}-126x+63x+189-x^{4}-3x^{3}-x^{4}+6x^{3}-9x^{2}-2x^{3}+12x^{2}-18x-x^{2}+6x-9.

$$\frac{8x^{3}-19x^{2}-75x+180-2x^{4}}{\left(x+3\right)\left(x-3\right)^{2}}$$

Expand \left(x+3\right)\left(x-3\right)^{2}.

$$\frac{8x^{3}-19x^{2}-75x+180-2x^{4}}{x^{3}-3x^{2}-9x+27}$$

Expand

$$\frac{180-75x-19x^{2}+8x^{3}-2x^{4}}{\left(x+3\right)\left(x-3\right)^{2}}$$

Short Solution Steps

Cancel out x in both numerator and denominator.

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

Add 2 and 5 to get 7.

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

Multiply \frac{x}{x-3} times \frac{x^{2}}{x-3} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply x-3 and x-3 to get \left(x-3\right)^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{\left(x-3\right)^{2}}{\left(x-3\right)^{2}}.

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

Since \frac{7\left(x-3\right)^{2}}{\left(x-3\right)^{2}} and \frac{x^{3}}{\left(x-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 7\left(x-3\right)^{2}-x^{3}.

$$\frac{7x^{2}-42x+63-x^{3}}{\left(x-3\right)^{2}}-\frac{\left(x+1\right)^{2}}{x+3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)^{2} and x+3 is \left(x+3\right)\left(x-3\right)^{2}. Multiply \frac{7x^{2}-42x+63-x^{3}}{\left(x-3\right)^{2}} times \frac{x+3}{x+3}. Multiply \frac{\left(x+1\right)^{2}}{x+3} times \frac{\left(x-3\right)^{2}}{\left(x-3\right)^{2}}.

$$\frac{\left(7x^{2}-42x+63-x^{3}\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)^{2}}-\frac{\left(x+1\right)^{2}\left(x-3\right)^{2}}{\left(x+3\right)\left(x-3\right)^{2}}$$

Since \frac{\left(7x^{2}-42x+63-x^{3}\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)^{2}} and \frac{\left(x+1\right)^{2}\left(x-3\right)^{2}}{\left(x+3\right)\left(x-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(7x^{2}-42x+63-x^{3}\right)\left(x+3\right)-\left(x+1\right)^{2}\left(x-3\right)^{2}}{\left(x+3\right)\left(x-3\right)^{2}}$$

Do the multiplications in \left(7x^{2}-42x+63-x^{3}\right)\left(x+3\right)-\left(x+1\right)^{2}\left(x-3\right)^{2}.

$$\frac{7x^{3}+21x^{2}-42x^{2}-126x+63x+189-x^{4}-3x^{3}-x^{4}+6x^{3}-9x^{2}-2x^{3}+12x^{2}-18x-x^{2}+6x-9}{\left(x+3\right)\left(x-3\right)^{2}}$$

Combine like terms in 7x^{3}+21x^{2}-42x^{2}-126x+63x+189-x^{4}-3x^{3}-x^{4}+6x^{3}-9x^{2}-2x^{3}+12x^{2}-18x-x^{2}+6x-9.

$$\frac{8x^{3}-19x^{2}-75x+180-2x^{4}}{\left(x+3\right)\left(x-3\right)^{2}}$$

Expand \left(x+3\right)\left(x-3\right)^{2}.

$$\frac{8x^{3}-19x^{2}-75x+180-2x^{4}}{x^{3}-3x^{2}-9x+27}$$