Question 144708
{{{(t+22)/(t^2-t-72)+(8)/(t-9)=(4)/(t+8)}}} Start with the given equation



{{{(t+22)/((t-9)(t+8))+(8)/(t-9)=(4)/(t+8)}}} Factor {{{t^2-t-72}}} to get {{{(t-9)(t+8)}}}




{{{((t-9)(t+8))((t+22)/((t-9)(t+8)))+((t-9)(t+8))((8)/(t-9))=((t-9)(t+8))((4)/(t+8))}}} Multiply <b>every</b> term by the LCD {{{(t-9)(t+8)}}} to clear out the fractions




{{{(cross((t-9))cross((t+8)))((t+22)/(cross((t-9))cross((t+8))))+(cross((t-9))(t+8))((8)/cross((t-9)))=((t-9)cross((t+8)))((4)/cross((t+8)))}}} Cancel like terms



{{{(t+22)+(t+8)8=(t-9)4}}} Simplify



{{{t+22+8t+64=4t-36}}} Distribute




{{{9t+86=4t-36}}} Combine like terms on the left side



{{{9t=4t-36-86}}}Subtract 86 from both sides



{{{9t-4t=-36-86}}} Subtract 4t from both sides



{{{5t=-36-86}}} Combine like terms on the left side



{{{5t=-122}}} Combine like terms on the right side



{{{t=(-122)/(5)}}} Divide both sides by 5 to isolate t




{{{t=-122/5}}} Reduce


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Answer:

So our answer is {{{t=-122/5}}}  (which is approximately {{{t=-24.4}}} in decimal form)