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\frac{-\left(4a+3b\right)}{-a+b}+\frac{5a+2b}{-a+b}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-b and b-a is -a+b. Multiply \frac{4a+3b}{a-b} times \frac{-1}{-1}.
\frac{-\left(4a+3b\right)+5a+2b}{-a+b}
Since \frac{-\left(4a+3b\right)}{-a+b} and \frac{5a+2b}{-a+b} have the same denominator, add them by adding their numerators.
\frac{-4a-3b+5a+2b}{-a+b}
Do the multiplications in -\left(4a+3b\right)+5a+2b.
\frac{a-b}{-a+b}
Combine like terms in -4a-3b+5a+2b.
\frac{-\left(-a+b\right)}{-a+b}
Extract the negative sign in a-b.
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Cancel out -a+b 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}