Question 188590
{{{(x^2+x-6)/(x^2+3x)}}} Start with the given expression



{{{((x+3)(x-2))/(x^2+3x)}}} Factor the numerator



{{{((x+3)(x-2))/(x(x+3))}}} Factor the denominator



{{{(cross((x+3))(x-2))/(x*cross((x+3)))}}} Cancel out the common terms.



{{{(x-2)/x}}} Simplify



So {{{(x^2+x-6)/(x^2+3x)=(x-2)/x}}} where {{{x<>0}}} or {{{x<>-3}}} (these are the restrictions). Note: These restrictions are made to avoid division by zero.




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{{{(4x^2-25)/(2x^2+3x-20)}}} Start with the given expression



{{{((2x+5)(2x-5))/(x^2+3x)}}} Factor the numerator



{{{((2x+5)(2x-5))/((x+4)(2x-5))}}} Factor the denominator



{{{((2x+5)cross((2x-5)))/((x+4)cross((2x-5)))}}} Cancel out the common terms.



{{{(2x+5)/(x+4)}}} Simplify



So {{{(4x^2-25)/(2x^2+3x-20)=(2x+5)/(x+4)}}} where {{{x<>-4}}} or {{{x<>5/2}}} (these are the restrictions). Note: These restrictions are made to avoid division by zero.