Question 188737
{{{(2/(x+3)+1)/(4/(x+3)+2)}}} Start with the given expression.



{{{(2/(x+3)+(x+3)/(x+3))/(4/(x+3)+2)}}} Multiply the term "1" in the numerator by {{{(x+3)/(x+3)}}}



{{{((2+x+3)/(x+3))/(4/(x+3)+2)}}} Combine the upper fractions.



{{{((x+5)/(x+3))/(4/(x+3)+2)}}} Combine like terms.



{{{((x+5)/(x+3))/(4/(x+3)+(2(x+3))/(x+3))}}} Multiply the term "2" in the denominator by {{{(x+3)/(x+3)}}}



{{{((x+5)/(x+3))/(4/(x+3)+(2x+6)/(x+3))}}} Distribute



{{{((x+5)/(x+3))/((4+2x+6)/(x+3))}}} Combine the lower fractions.



{{{((x+5)/(x+3))/((2x+10)/(x+3))}}} Combine like terms.



{{{((x+5)/(x+3))*((x+3)/(2x+10))}}} Multiply the upper fraction by the reciprocal of the lower fraction.



{{{((x+5)/(x+3))*((x+3)/(2(x+5)))}}} Factor {{{2x+10}}} to get {{{2(x+5)}}}



{{{((x+5)(x+3))/(2(x+3)(x+5)))}}} Combine the fractions.



{{{(highlight((x+5))highlight((x+3)))/(2*highlight((x+3))highlight((x+5))))}}} Highlight the common terms.



{{{(cross((x+5))cross((x+3)))/(2*cross((x+3))cross((x+5))))}}} Cancel out the common terms.



{{{1/2}}} Simplify



So {{{(2/(x+3)+1)/(4/(x+3)+2)}}} simplifies to {{{1/2}}}



In other words,  {{{(2/(x+3)+1)/(4/(x+3)+2)=1/2}}} where {{{x<>-5}}} or {{{x<>-3}}}




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Note: in this case, the problem can be simplified in another way:



{{{(2/(x+3)+1)/(4/(x+3)+2)}}} Start with the given expression.



{{{(2/(x+3)+1)/(2(2/(x+3)+1))}}} Factor out the GCF {{{2}}} from the denominator



{{{highlight(2/(x+3)+1)/(2*highlight((2/(x+3)+1)))}}} Highlight the common terms.



{{{cross(2/(x+3)+1)/(2*cross((2/(x+3)+1)))}}} Cancel out the common terms.



{{{1/2}}} Simplify



So {{{(2/(x+3)+1)/(4/(x+3)+2)=1/2}}} where {{{x<>-5}}} or {{{x<>-3}}}



Note: this technique does not always apply.