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\frac{\left(\frac{x-2}{x-2}+\frac{4}{x-2}\right)\left(x-4+\frac{4}{x}\right)-3}{\frac{4}{x}-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-2}{x-2}.
\frac{\frac{x-2+4}{x-2}\left(x-4+\frac{4}{x}\right)-3}{\frac{4}{x}-1}
Since \frac{x-2}{x-2} and \frac{4}{x-2} have the same denominator, add them by adding their numerators.
\frac{\frac{x+2}{x-2}\left(x-4+\frac{4}{x}\right)-3}{\frac{4}{x}-1}
Combine like terms in x-2+4.
\frac{\frac{x+2}{x-2}\left(\frac{\left(x-4\right)x}{x}+\frac{4}{x}\right)-3}{\frac{4}{x}-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply x-4 times \frac{x}{x}.
\frac{\frac{x+2}{x-2}\times \frac{\left(x-4\right)x+4}{x}-3}{\frac{4}{x}-1}
Since \frac{\left(x-4\right)x}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.
\frac{\frac{x+2}{x-2}\times \frac{x^{2}-4x+4}{x}-3}{\frac{4}{x}-1}
Do the multiplications in \left(x-4\right)x+4.
\frac{\frac{\left(x+2\right)\left(x^{2}-4x+4\right)}{\left(x-2\right)x}-3}{\frac{4}{x}-1}
Multiply \frac{x+2}{x-2} times \frac{x^{2}-4x+4}{x} by multiplying numerator times numerator and denominator times denominator.
\frac{\frac{\left(x+2\right)\left(x^{2}-4x+4\right)}{\left(x-2\right)x}-\frac{3\left(x-2\right)x}{\left(x-2\right)x}}{\frac{4}{x}-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{\left(x-2\right)x}{\left(x-2\right)x}.
\frac{\frac{\left(x+2\right)\left(x^{2}-4x+4\right)-3\left(x-2\right)x}{\left(x-2\right)x}}{\frac{4}{x}-1}
Since \frac{\left(x+2\right)\left(x^{2}-4x+4\right)}{\left(x-2\right)x} and \frac{3\left(x-2\right)x}{\left(x-2\right)x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x^{3}-4x^{2}+4x+2x^{2}-8x+8-3x^{2}+6x}{\left(x-2\right)x}}{\frac{4}{x}-1}
Do the multiplications in \left(x+2\right)\left(x^{2}-4x+4\right)-3\left(x-2\right)x.
\frac{\frac{x^{3}-5x^{2}+2x+8}{\left(x-2\right)x}}{\frac{4}{x}-1}
Combine like terms in x^{3}-4x^{2}+4x+2x^{2}-8x+8-3x^{2}+6x.
\frac{\frac{\left(x-4\right)\left(x-2\right)\left(x+1\right)}{x\left(x-2\right)}}{\frac{4}{x}-1}
Factor the expressions that are not already factored in \frac{x^{3}-5x^{2}+2x+8}{\left(x-2\right)x}.
\frac{\frac{\left(x-4\right)\left(x+1\right)}{x}}{\frac{4}{x}-1}
Cancel out x-2 in both numerator and denominator.
\frac{\frac{\left(x-4\right)\left(x+1\right)}{x}}{\frac{4}{x}-\frac{x}{x}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.
\frac{\frac{\left(x-4\right)\left(x+1\right)}{x}}{\frac{4-x}{x}}
Since \frac{4}{x} and \frac{x}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(x-4\right)\left(x+1\right)x}{x\left(4-x\right)}
Divide \frac{\left(x-4\right)\left(x+1\right)}{x} by \frac{4-x}{x} by multiplying \frac{\left(x-4\right)\left(x+1\right)}{x} by the reciprocal of \frac{4-x}{x}.
\frac{-x\left(x+1\right)\left(-x+4\right)}{x\left(-x+4\right)}
Extract the negative sign in x-4.
-\left(x+1\right)
Cancel out x\left(-x+4\right) in both numerator and denominator.
-x-1
To find the opposite of x+1, find the opposite of each term.
\frac{\left(\frac{x-2}{x-2}+\frac{4}{x-2}\right)\left(x-4+\frac{4}{x}\right)-3}{\frac{4}{x}-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-2}{x-2}.
\frac{\frac{x-2+4}{x-2}\left(x-4+\frac{4}{x}\right)-3}{\frac{4}{x}-1}
Since \frac{x-2}{x-2} and \frac{4}{x-2} have the same denominator, add them by adding their numerators.
\frac{\frac{x+2}{x-2}\left(x-4+\frac{4}{x}\right)-3}{\frac{4}{x}-1}
Combine like terms in x-2+4.
\frac{\frac{x+2}{x-2}\left(\frac{\left(x-4\right)x}{x}+\frac{4}{x}\right)-3}{\frac{4}{x}-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply x-4 times \frac{x}{x}.
\frac{\frac{x+2}{x-2}\times \frac{\left(x-4\right)x+4}{x}-3}{\frac{4}{x}-1}
Since \frac{\left(x-4\right)x}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.
\frac{\frac{x+2}{x-2}\times \frac{x^{2}-4x+4}{x}-3}{\frac{4}{x}-1}
Do the multiplications in \left(x-4\right)x+4.
\frac{\frac{\left(x+2\right)\left(x^{2}-4x+4\right)}{\left(x-2\right)x}-3}{\frac{4}{x}-1}
Multiply \frac{x+2}{x-2} times \frac{x^{2}-4x+4}{x} by multiplying numerator times numerator and denominator times denominator.
\frac{\frac{\left(x+2\right)\left(x^{2}-4x+4\right)}{\left(x-2\right)x}-\frac{3\left(x-2\right)x}{\left(x-2\right)x}}{\frac{4}{x}-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{\left(x-2\right)x}{\left(x-2\right)x}.
\frac{\frac{\left(x+2\right)\left(x^{2}-4x+4\right)-3\left(x-2\right)x}{\left(x-2\right)x}}{\frac{4}{x}-1}
Since \frac{\left(x+2\right)\left(x^{2}-4x+4\right)}{\left(x-2\right)x} and \frac{3\left(x-2\right)x}{\left(x-2\right)x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x^{3}-4x^{2}+4x+2x^{2}-8x+8-3x^{2}+6x}{\left(x-2\right)x}}{\frac{4}{x}-1}
Do the multiplications in \left(x+2\right)\left(x^{2}-4x+4\right)-3\left(x-2\right)x.
\frac{\frac{x^{3}-5x^{2}+2x+8}{\left(x-2\right)x}}{\frac{4}{x}-1}
Combine like terms in x^{3}-4x^{2}+4x+2x^{2}-8x+8-3x^{2}+6x.
\frac{\frac{\left(x-4\right)\left(x-2\right)\left(x+1\right)}{x\left(x-2\right)}}{\frac{4}{x}-1}
Factor the expressions that are not already factored in \frac{x^{3}-5x^{2}+2x+8}{\left(x-2\right)x}.
\frac{\frac{\left(x-4\right)\left(x+1\right)}{x}}{\frac{4}{x}-1}
Cancel out x-2 in both numerator and denominator.
\frac{\frac{\left(x-4\right)\left(x+1\right)}{x}}{\frac{4}{x}-\frac{x}{x}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.
\frac{\frac{\left(x-4\right)\left(x+1\right)}{x}}{\frac{4-x}{x}}
Since \frac{4}{x} and \frac{x}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(x-4\right)\left(x+1\right)x}{x\left(4-x\right)}
Divide \frac{\left(x-4\right)\left(x+1\right)}{x} by \frac{4-x}{x} by multiplying \frac{\left(x-4\right)\left(x+1\right)}{x} by the reciprocal of \frac{4-x}{x}.
\frac{-x\left(x+1\right)\left(-x+4\right)}{x\left(-x+4\right)}
Extract the negative sign in x-4.
-\left(x+1\right)
Cancel out x\left(-x+4\right) in both numerator and denominator.
-x-1
To find the opposite of x+1, find the opposite of each term.