Evaluate
-\frac{5}{3}\approx -1.666666667
Factor
-\frac{5}{3} = -1\frac{2}{3} = -1.6666666666666667
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\frac{5\left(\sqrt{7}-1\right)}{\left(\sqrt{7}+1\right)\left(\sqrt{7}-1\right)}-\frac{5}{\sqrt{7}-1}
Rationalize the denominator of \frac{5}{\sqrt{7}+1} by multiplying numerator and denominator by \sqrt{7}-1.
\frac{5\left(\sqrt{7}-1\right)}{\left(\sqrt{7}\right)^{2}-1^{2}}-\frac{5}{\sqrt{7}-1}
Consider \left(\sqrt{7}+1\right)\left(\sqrt{7}-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{5\left(\sqrt{7}-1\right)}{7-1}-\frac{5}{\sqrt{7}-1}
Square \sqrt{7}. Square 1.
\frac{5\left(\sqrt{7}-1\right)}{6}-\frac{5}{\sqrt{7}-1}
Subtract 1 from 7 to get 6.
\frac{5\left(\sqrt{7}-1\right)}{6}-\frac{5\left(\sqrt{7}+1\right)}{\left(\sqrt{7}-1\right)\left(\sqrt{7}+1\right)}
Rationalize the denominator of \frac{5}{\sqrt{7}-1} by multiplying numerator and denominator by \sqrt{7}+1.
\frac{5\left(\sqrt{7}-1\right)}{6}-\frac{5\left(\sqrt{7}+1\right)}{\left(\sqrt{7}\right)^{2}-1^{2}}
Consider \left(\sqrt{7}-1\right)\left(\sqrt{7}+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{5\left(\sqrt{7}-1\right)}{6}-\frac{5\left(\sqrt{7}+1\right)}{7-1}
Square \sqrt{7}. Square 1.
\frac{5\left(\sqrt{7}-1\right)}{6}-\frac{5\left(\sqrt{7}+1\right)}{6}
Subtract 1 from 7 to get 6.
\frac{5\left(\sqrt{7}-1\right)-5\left(\sqrt{7}+1\right)}{6}
Since \frac{5\left(\sqrt{7}-1\right)}{6} and \frac{5\left(\sqrt{7}+1\right)}{6} have the same denominator, subtract them by subtracting their numerators.
\frac{5\sqrt{7}-5-5\sqrt{7}-5}{6}
Do the multiplications in 5\left(\sqrt{7}-1\right)-5\left(\sqrt{7}+1\right).
\frac{-10}{6}
Do the calculations in 5\sqrt{7}-5-5\sqrt{7}-5.
-\frac{5}{3}
Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.
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
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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}