How do you simplify #\frac { 5v } { v ^ { 2} - 13v + 36} - \frac { 4} { v ^ { 2} - 14v + 45}#?

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Answer 1 · 2016-10-25T17:45:20

Factor the denominator to see what our LCD (Least common denominator) will be.

#=(5v)/((v - 9)(v - 4)) - 4/((v - 9)(v - 5))#

#:.# The LCD is #(v - 9)(v - 4)(v - 5), v!=9, 4, 5#.

#=(5v(v - 5))/((v - 9)(v - 4)(v - 5)) - (4(v - 4))/((v - 9)(v - 5)(v - 4))#

#=(5v^2 - 25v - 4v + 16)/((v - 9)(v - 4)(v - 5))#

#=(5v^2 - 29v + 16)/((v - 9)(v - 4)(v - 5))#

This is far as we can simplify, since neither the numerator nor the denominator may be factored any more.

Hopefully this helps!