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Mathematics
OpenStudy (anonymous):

Simplify. 1+(2)/(y)/1-(4)/(y^2)

OpenStudy (anonymous):

-4y^3 + 2/y/+ 1

OpenStudy (anonymous):

Jim...thanks for jumping in.

jimthompson5910 (jim_thompson5910):

np hang on one sec

jimthompson5910 (jim_thompson5910):

\[\large \frac{1+\frac{2}{y}}{1-\frac{4}{y^2}}\] \[\large \frac{y^2*1+y^2*\frac{2}{y}}{y^2*1-y^2*\frac{4}{y^2}}\] \[\large \frac{y^2+2y}{y^2-4}\] \[\large \frac{y(y+2)}{(y+2)(y-2)}\] \[\large \frac{y\cancel{(y+2)}}{\cancel{(y+2)}(y-2)}\] \[\large \frac{y}{y-2}\] So \[\large \frac{1+\frac{2}{y}}{1-\frac{4}{y^2}}=\frac{y}{y-2}\]

jimthompson5910 (jim_thompson5910):

In the second step, I multiplied EVERY term by the inner LCD y^2 to clear out the inner fractions. From there I factored and simplified.

OpenStudy (anonymous):

Good job.

jimthompson5910 (jim_thompson5910):

thx

OpenStudy (anonymous):

You are really smart. I am a fan.

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