Evaluate
\frac{47}{\left(x-7\right)\left(x-2\right)}
Expand
\frac{47}{\left(x-7\right)\left(x-2\right)}
Graph
Quiz
Polynomial
5 problems similar to:
\frac { 6 x + 5 } { x ^ { 2 } - 9 x + 14 } - \frac { 6 } { x - 2 }
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\frac{6x+5}{\left(x-7\right)\left(x-2\right)}-\frac{6}{x-2}
Factor x^{2}-9x+14.
\frac{6x+5}{\left(x-7\right)\left(x-2\right)}-\frac{6\left(x-7\right)}{\left(x-7\right)\left(x-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-7\right)\left(x-2\right) and x-2 is \left(x-7\right)\left(x-2\right). Multiply \frac{6}{x-2} times \frac{x-7}{x-7}.
\frac{6x+5-6\left(x-7\right)}{\left(x-7\right)\left(x-2\right)}
Since \frac{6x+5}{\left(x-7\right)\left(x-2\right)} and \frac{6\left(x-7\right)}{\left(x-7\right)\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x+5-6x+42}{\left(x-7\right)\left(x-2\right)}
Do the multiplications in 6x+5-6\left(x-7\right).
\frac{47}{\left(x-7\right)\left(x-2\right)}
Combine like terms in 6x+5-6x+42.
\frac{47}{x^{2}-9x+14}
Expand \left(x-7\right)\left(x-2\right).
\frac{6x+5}{\left(x-7\right)\left(x-2\right)}-\frac{6}{x-2}
Factor x^{2}-9x+14.
\frac{6x+5}{\left(x-7\right)\left(x-2\right)}-\frac{6\left(x-7\right)}{\left(x-7\right)\left(x-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-7\right)\left(x-2\right) and x-2 is \left(x-7\right)\left(x-2\right). Multiply \frac{6}{x-2} times \frac{x-7}{x-7}.
\frac{6x+5-6\left(x-7\right)}{\left(x-7\right)\left(x-2\right)}
Since \frac{6x+5}{\left(x-7\right)\left(x-2\right)} and \frac{6\left(x-7\right)}{\left(x-7\right)\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x+5-6x+42}{\left(x-7\right)\left(x-2\right)}
Do the multiplications in 6x+5-6\left(x-7\right).
\frac{47}{\left(x-7\right)\left(x-2\right)}
Combine like terms in 6x+5-6x+42.
\frac{47}{x^{2}-9x+14}
Expand \left(x-7\right)\left(x-2\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
Arithmetic
699 * 533
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\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}