Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac{25x^{3}-36x}{6x^{2}-31x+30}$$

Answer

$$(x*(5*x+6)*(5*x-6))/(6*x^2-31*x+30)$$

Solution


Factor out the common term \(x\).
\[\frac{x(25{x}^{2}-36)}{6{x}^{2}-31x+30}\]
Rewrite \(25{x}^{2}-36\) in the form \({a}^{2}-{b}^{2}\), where \(a=5x\) and \(b=6\).
\[\frac{x({(5x)}^{2}-{6}^{2})}{6{x}^{2}-31x+30}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[\frac{x(5x+6)(5x-6)}{6{x}^{2}-31x+30}\]
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