2- \frac{ 9 }{ 4 } -2(4- \frac{ 9 }{ 4 } )+ \frac{ 3 }{ 2 } (2- \frac{ 9 }{ 4 }
Evaluate
-\frac{33}{8}=-4.125
Factor
-\frac{33}{8} = -4\frac{1}{8} = -4.125
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\frac{8}{4}-\frac{9}{4}-2\left(4-\frac{9}{4}\right)+\frac{3}{2}\left(2-\frac{9}{4}\right)
Convert 2 to fraction \frac{8}{4}.
\frac{8-9}{4}-2\left(4-\frac{9}{4}\right)+\frac{3}{2}\left(2-\frac{9}{4}\right)
Since \frac{8}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.
-\frac{1}{4}-2\left(4-\frac{9}{4}\right)+\frac{3}{2}\left(2-\frac{9}{4}\right)
Subtract 9 from 8 to get -1.
-\frac{1}{4}-2\left(\frac{16}{4}-\frac{9}{4}\right)+\frac{3}{2}\left(2-\frac{9}{4}\right)
Convert 4 to fraction \frac{16}{4}.
-\frac{1}{4}-2\times \frac{16-9}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)
Since \frac{16}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.
-\frac{1}{4}-2\times \frac{7}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)
Subtract 9 from 16 to get 7.
-\frac{1}{4}-\frac{2\times 7}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)
Express 2\times \frac{7}{4} as a single fraction.
-\frac{1}{4}-\frac{14}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)
Multiply 2 and 7 to get 14.
\frac{-1-14}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)
Since -\frac{1}{4} and \frac{14}{4} have the same denominator, subtract them by subtracting their numerators.
-\frac{15}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)
Subtract 14 from -1 to get -15.
-\frac{15}{4}+\frac{3}{2}\left(\frac{8}{4}-\frac{9}{4}\right)
Convert 2 to fraction \frac{8}{4}.
-\frac{15}{4}+\frac{3}{2}\times \frac{8-9}{4}
Since \frac{8}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.
-\frac{15}{4}+\frac{3}{2}\left(-\frac{1}{4}\right)
Subtract 9 from 8 to get -1.
-\frac{15}{4}+\frac{3\left(-1\right)}{2\times 4}
Multiply \frac{3}{2} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.
-\frac{15}{4}+\frac{-3}{8}
Do the multiplications in the fraction \frac{3\left(-1\right)}{2\times 4}.
-\frac{15}{4}-\frac{3}{8}
Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.
-\frac{30}{8}-\frac{3}{8}
Least common multiple of 4 and 8 is 8. Convert -\frac{15}{4} and \frac{3}{8} to fractions with denominator 8.
\frac{-30-3}{8}
Since -\frac{30}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.
-\frac{33}{8}
Subtract 3 from -30 to get -33.
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}