How do you multiply and simplify #\frac { t^ { 2} - r ^ { 2} } { t ^ { 2} + t r - 2r ^ { 2} } \cdot \frac { t ^ { 2} + 3t r + 2r ^ { 2} } { t ^ { 2} + 2tr + r ^ { 2} }#?

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Answer 1 · 2017-05-06T09:23:43

1

#rArr[(t+r)(t-r)}/[t^2+(2-1)tr-2r^2].[t^2+(2+1)tr+2r^2]/(t+r)^2#

#rArr[(t+r)(t-r)]/[t^2+2tr-tr-2r^2].[t^2+2tr+tr+2r^2]/[(t+r)^2]#

#rArr[(t+r)(t-r)]/[t(t+2r)-r(t+2r)].[t(t+2r)+r(t+2r)]/[(t+r)^2]#

#rArr[(t+r)(t-r)]/[(t+2r)(t-r)].[(t+2r)(t+r)]/[(t+r)^2]#

#rArr[cancel(t+r)cancel(t+r)cancel(t+2r)cancel(t-r)]/[cancel(t+2r)cancel(t-r)cancel{(t+r)}^2]#

#rArr 1#

Answer 2 · 2017-05-06T10:28:03

#color(blue)1#

#(t^2-r^2)/(t^2+tr-2r^2)*(t^2+3tr+2r^2)/(t^2+2tr+r^2)#

#:.=((cancel(t-r))(cancel(t+r)))/((cancel(t+2r))(cancel(t-r)))*((cancel(t+r))(cancel(t+2r)))/((cancel(t+r))(cancel(t+r)))#

#:.=color(blue)1#