Question

What expression is equivalent to the expression below ?m+3/m^2-16/m^2-9/m+4

Answer 1

`\large\boxed{(1)/((m-4)(m-3))=(1)/(m^2-7m+12)}`

Explanation:

`((m+3)/(m^2-16))/((m^2-9)/(m+4))=(m+3)/(m^2-16)\cdot(m+4)/(m^2-9)=(*)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\m^2-16=m^2=4^2=(m-4)(m+4)\\m^2-9=m^2-3^2=(m-3)(m+3)\\\\(*)=(m+3)/((m-4)(m+4))\cdot(m+4)/((m-3)(m+3))\\\\\text{cancel}\ (m+3)\ \text{and}\ (m+4)\\\\=(1)/(m-4)\cdot(1)/(m-3)=(1)/((m-4)(m-3))\\\\\text{use\ FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(1)/((m)(m)+(m)(-3)+(-4)(m)+(-4)(-3))\\\\=(1)/(m^2-3m-4m+12)=(1)/(m^2-7m+12)`