Evaluate
\frac{3\left(x-6\right)\left(x-1\right)}{\left(x-3\right)^{2}}
Expand
\frac{3\left(x^{2}-7x+6\right)}{\left(x-3\right)^{2}}
Graph
Share
Copied to clipboard
\frac{3x}{x-3}-\frac{12x-18}{\left(x-3\right)^{2}}
Factor x^{2}-6x+9.
\frac{3x\left(x-3\right)}{\left(x-3\right)^{2}}-\frac{12x-18}{\left(x-3\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and \left(x-3\right)^{2} is \left(x-3\right)^{2}. Multiply \frac{3x}{x-3} times \frac{x-3}{x-3}.
\frac{3x\left(x-3\right)-\left(12x-18\right)}{\left(x-3\right)^{2}}
Since \frac{3x\left(x-3\right)}{\left(x-3\right)^{2}} and \frac{12x-18}{\left(x-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}-9x-12x+18}{\left(x-3\right)^{2}}
Do the multiplications in 3x\left(x-3\right)-\left(12x-18\right).
\frac{3x^{2}-21x+18}{\left(x-3\right)^{2}}
Combine like terms in 3x^{2}-9x-12x+18.
\frac{3x^{2}-21x+18}{x^{2}-6x+9}
Expand \left(x-3\right)^{2}.
\frac{3x}{x-3}-\frac{12x-18}{\left(x-3\right)^{2}}
Factor x^{2}-6x+9.
\frac{3x\left(x-3\right)}{\left(x-3\right)^{2}}-\frac{12x-18}{\left(x-3\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and \left(x-3\right)^{2} is \left(x-3\right)^{2}. Multiply \frac{3x}{x-3} times \frac{x-3}{x-3}.
\frac{3x\left(x-3\right)-\left(12x-18\right)}{\left(x-3\right)^{2}}
Since \frac{3x\left(x-3\right)}{\left(x-3\right)^{2}} and \frac{12x-18}{\left(x-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}-9x-12x+18}{\left(x-3\right)^{2}}
Do the multiplications in 3x\left(x-3\right)-\left(12x-18\right).
\frac{3x^{2}-21x+18}{\left(x-3\right)^{2}}
Combine like terms in 3x^{2}-9x-12x+18.
\frac{3x^{2}-21x+18}{x^{2}-6x+9}
Expand \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}