Question 174872
{{{(x-5)/(x^2-4)-3x/(4x(2-x))}}} Start with the given expression.



{{{(x-5)/((x+2)(x-2))-3x/(4x(2-x))}}} Factor the first denominator {{{x^2-4}}} to get {{{(x+2)(x-2)}}}



{{{(x-5)/((x+2)(x-2))-3x/(-4x(x-2))}}} Factor the second denominator {{{4x(2-x)}}} to get {{{-4x(x-2)}}}



{{{(x-5)/((x+2)(x-2))+3x/(4x(x-2))}}} Reduce



Take note that the LCD is {{{4x(x+2)(x-2)}}}



{{{(4x(x-5))/(4x(x+2)(x-2))+3x/(4x(x-2))}}} Multiply the first fraction by {{{(4x)/(4x)}}} (to get the denominator equal to the LCD)




{{{(4x(x-5))/(4x(x+2)(x-2))+(3x(x+2))/(4x(x+2)(x-2))}}} Multiply the second fraction by {{{(x+2)/(x+2)}}} (to get the denominator equal to the LCD)



{{{(4x^2-20x)/(4x(x+2)(x-2))+(3x^2+6x)/(4x(x+2)(x-2))}}} Distribute



{{{(4x^2-20x+3x^2+6x)/(4x(x+2)(x-2))}}} Add the fractions. This is now possible because the fractions have equal denominators.



{{{(7x^2-14x)/(4x(x+2)(x-2))}}} Combine like terms.



{{{(7x(x-2))/(4x(x+2)(x-2))}}} Factor out the GCF {{{7x}}}



{{{(7*highlight(x)*highlight((x-2)))/(4*highlight(x)(x+2)highlight((x-2)))}}} Highlight the common terms.



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



{{{(7)/(4(x+2))}}} Simplify



{{{(7)/(4x+8)}}} Distribute




So {{{(x-5)/(x^2-4)-3x/(4x(2-x))}}} simplifies to {{{(7)/(4x+8)}}}



In other words, {{{(x-5)/(x^2-4)-3x/(4x(2-x))=(7)/(4x+8)}}} where {{{x<>-2}}}, {{{x<>0}}}, or {{{x<>2}}}