Evaluate
\frac{\left(1-x\right)\left(x+3\right)}{4}
Expand
-\frac{x^{2}}{4}-\frac{x}{2}+\frac{3}{4}
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\left(\frac{1}{4}+\frac{1}{4}\left(-1\right)x\right)\left(x+3\right)
Use the distributive property to multiply \frac{1}{4} by 1-x.
\left(\frac{1}{4}-\frac{1}{4}x\right)\left(x+3\right)
Multiply \frac{1}{4} and -1 to get -\frac{1}{4}.
\frac{1}{4}x+\frac{1}{4}\times 3-\frac{1}{4}xx-\frac{1}{4}x\times 3
Apply the distributive property by multiplying each term of \frac{1}{4}-\frac{1}{4}x by each term of x+3.
\frac{1}{4}x+\frac{1}{4}\times 3-\frac{1}{4}x^{2}-\frac{1}{4}x\times 3
Multiply x and x to get x^{2}.
\frac{1}{4}x+\frac{3}{4}-\frac{1}{4}x^{2}-\frac{1}{4}x\times 3
Multiply \frac{1}{4} and 3 to get \frac{3}{4}.
\frac{1}{4}x+\frac{3}{4}-\frac{1}{4}x^{2}+\frac{-3}{4}x
Express -\frac{1}{4}\times 3 as a single fraction.
\frac{1}{4}x+\frac{3}{4}-\frac{1}{4}x^{2}-\frac{3}{4}x
Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.
-\frac{1}{2}x+\frac{3}{4}-\frac{1}{4}x^{2}
Combine \frac{1}{4}x and -\frac{3}{4}x to get -\frac{1}{2}x.
\left(\frac{1}{4}+\frac{1}{4}\left(-1\right)x\right)\left(x+3\right)
Use the distributive property to multiply \frac{1}{4} by 1-x.
\left(\frac{1}{4}-\frac{1}{4}x\right)\left(x+3\right)
Multiply \frac{1}{4} and -1 to get -\frac{1}{4}.
\frac{1}{4}x+\frac{1}{4}\times 3-\frac{1}{4}xx-\frac{1}{4}x\times 3
Apply the distributive property by multiplying each term of \frac{1}{4}-\frac{1}{4}x by each term of x+3.
\frac{1}{4}x+\frac{1}{4}\times 3-\frac{1}{4}x^{2}-\frac{1}{4}x\times 3
Multiply x and x to get x^{2}.
\frac{1}{4}x+\frac{3}{4}-\frac{1}{4}x^{2}-\frac{1}{4}x\times 3
Multiply \frac{1}{4} and 3 to get \frac{3}{4}.
\frac{1}{4}x+\frac{3}{4}-\frac{1}{4}x^{2}+\frac{-3}{4}x
Express -\frac{1}{4}\times 3 as a single fraction.
\frac{1}{4}x+\frac{3}{4}-\frac{1}{4}x^{2}-\frac{3}{4}x
Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.
-\frac{1}{2}x+\frac{3}{4}-\frac{1}{4}x^{2}
Combine \frac{1}{4}x and -\frac{3}{4}x to get -\frac{1}{2}x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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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}