Example

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

Question

$$\frac{2}{(x-2)(x-3)}+\frac{2}{(x-1)(3-x)}+\frac{1}{(1-x)(2-x)^{2}}$$

Answer

$$(2*(x-1)*(3-x)*(1-x)*(2-x)^2+2*(x-2)*(x-3)*(1-x)*(2-x)^2+(x-2)*(x-3)*(x-1)*(3-x))/((x-2)*(x-3)*(x-1)*(3-x)*(1-x)*(2-x)^2)$$

Solution


Rewrite the expression with a common denominator.
\[\frac{2(x-1)(3-x)(1-x){(2-x)}^{2}+2(x-2)(x-3)(1-x){(2-x)}^{2}+(x-2)(x-3)(x-1)(3-x)}{(x-2)(x-3)(x-1)(3-x)(1-x){(2-x)}^{2}}\]
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