Evaluate
\frac{4x^{2}-9x+8}{\left(3x-4\right)\left(4x-3\right)}
Differentiate w.r.t. x
\frac{4\left(2x^{2}-24x+23\right)}{144x^{4}-600x^{3}+913x^{2}-600x+144}
Graph
Share
Copied to clipboard
\frac{x\left(4x-3\right)}{\left(3x-4\right)\left(4x-3\right)}-\frac{2\left(3x-4\right)}{\left(3x-4\right)\left(4x-3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x-4 and 4x-3 is \left(3x-4\right)\left(4x-3\right). Multiply \frac{x}{3x-4} times \frac{4x-3}{4x-3}. Multiply \frac{2}{4x-3} times \frac{3x-4}{3x-4}.
\frac{x\left(4x-3\right)-2\left(3x-4\right)}{\left(3x-4\right)\left(4x-3\right)}
Since \frac{x\left(4x-3\right)}{\left(3x-4\right)\left(4x-3\right)} and \frac{2\left(3x-4\right)}{\left(3x-4\right)\left(4x-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x^{2}-3x-6x+8}{\left(3x-4\right)\left(4x-3\right)}
Do the multiplications in x\left(4x-3\right)-2\left(3x-4\right).
\frac{4x^{2}-9x+8}{\left(3x-4\right)\left(4x-3\right)}
Combine like terms in 4x^{2}-3x-6x+8.
\frac{4x^{2}-9x+8}{12x^{2}-25x+12}
Expand \left(3x-4\right)\left(4x-3\right).
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}