Evaluate
\frac{10x-33}{4\left(x-3\right)^{2}}
Expand
\frac{10x-33}{4\left(x-3\right)^{2}}
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\frac{5}{2\left(x-3\right)}-\frac{3}{\left(2x-6\right)^{2}}
Factor 2x-6.
\frac{5\times 2\left(x-3\right)}{4\left(x-3\right)^{2}}-\frac{3}{4\left(x-3\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-3\right) and \left(2x-6\right)^{2} is 4\left(x-3\right)^{2}. Multiply \frac{5}{2\left(x-3\right)} times \frac{2\left(x-3\right)}{2\left(x-3\right)}.
\frac{5\times 2\left(x-3\right)-3}{4\left(x-3\right)^{2}}
Since \frac{5\times 2\left(x-3\right)}{4\left(x-3\right)^{2}} and \frac{3}{4\left(x-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{10x-30-3}{4\left(x-3\right)^{2}}
Do the multiplications in 5\times 2\left(x-3\right)-3.
\frac{10x-33}{4\left(x-3\right)^{2}}
Combine like terms in 10x-30-3.
\frac{10x-33}{4x^{2}-24x+36}
Expand 4\left(x-3\right)^{2}.
\frac{5}{2\left(x-3\right)}-\frac{3}{\left(2x-6\right)^{2}}
Factor 2x-6.
\frac{5\times 2\left(x-3\right)}{4\left(x-3\right)^{2}}-\frac{3}{4\left(x-3\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-3\right) and \left(2x-6\right)^{2} is 4\left(x-3\right)^{2}. Multiply \frac{5}{2\left(x-3\right)} times \frac{2\left(x-3\right)}{2\left(x-3\right)}.
\frac{5\times 2\left(x-3\right)-3}{4\left(x-3\right)^{2}}
Since \frac{5\times 2\left(x-3\right)}{4\left(x-3\right)^{2}} and \frac{3}{4\left(x-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{10x-30-3}{4\left(x-3\right)^{2}}
Do the multiplications in 5\times 2\left(x-3\right)-3.
\frac{10x-33}{4\left(x-3\right)^{2}}
Combine like terms in 10x-30-3.
\frac{10x-33}{4x^{2}-24x+36}
Expand 4\left(x-3\right)^{2}.
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}