Evaluate
-\frac{a}{a-4}
Expand
-\frac{a}{a-4}
Share
Copied to clipboard
\frac{\frac{4a-1}{a+1}+\frac{\left(-a+1\right)\left(a+1\right)}{a+1}}{\frac{a^{2}-8a+16}{a+1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply -a+1 times \frac{a+1}{a+1}.
\frac{\frac{4a-1+\left(-a+1\right)\left(a+1\right)}{a+1}}{\frac{a^{2}-8a+16}{a+1}}
Since \frac{4a-1}{a+1} and \frac{\left(-a+1\right)\left(a+1\right)}{a+1} have the same denominator, add them by adding their numerators.
\frac{\frac{4a-1-a^{2}-a+a+1}{a+1}}{\frac{a^{2}-8a+16}{a+1}}
Do the multiplications in 4a-1+\left(-a+1\right)\left(a+1\right).
\frac{\frac{4a-a^{2}}{a+1}}{\frac{a^{2}-8a+16}{a+1}}
Combine like terms in 4a-1-a^{2}-a+a+1.
\frac{\left(4a-a^{2}\right)\left(a+1\right)}{\left(a+1\right)\left(a^{2}-8a+16\right)}
Divide \frac{4a-a^{2}}{a+1} by \frac{a^{2}-8a+16}{a+1} by multiplying \frac{4a-a^{2}}{a+1} by the reciprocal of \frac{a^{2}-8a+16}{a+1}.
\frac{-a^{2}+4a}{a^{2}-8a+16}
Cancel out a+1 in both numerator and denominator.
\frac{\frac{4a-1}{a+1}+\frac{\left(-a+1\right)\left(a+1\right)}{a+1}}{\frac{a^{2}-8a+16}{a+1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply -a+1 times \frac{a+1}{a+1}.
\frac{\frac{4a-1+\left(-a+1\right)\left(a+1\right)}{a+1}}{\frac{a^{2}-8a+16}{a+1}}
Since \frac{4a-1}{a+1} and \frac{\left(-a+1\right)\left(a+1\right)}{a+1} have the same denominator, add them by adding their numerators.
\frac{\frac{4a-1-a^{2}-a+a+1}{a+1}}{\frac{a^{2}-8a+16}{a+1}}
Do the multiplications in 4a-1+\left(-a+1\right)\left(a+1\right).
\frac{\frac{4a-a^{2}}{a+1}}{\frac{a^{2}-8a+16}{a+1}}
Combine like terms in 4a-1-a^{2}-a+a+1.
\frac{\left(4a-a^{2}\right)\left(a+1\right)}{\left(a+1\right)\left(a^{2}-8a+16\right)}
Divide \frac{4a-a^{2}}{a+1} by \frac{a^{2}-8a+16}{a+1} by multiplying \frac{4a-a^{2}}{a+1} by the reciprocal of \frac{a^{2}-8a+16}{a+1}.
\frac{-a^{2}+4a}{a^{2}-8a+16}
Cancel out a+1 in both numerator and denominator.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}