How do you solve #\frac { 1} { m - 4} = \frac { 6} { m ^ { 2} - 16}#?

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Answer 1 · 2017-09-01T13:36:02

#m = 2#

You have an equation with one fraction on each side.
Note the restrictions: #m !=4 and m!=-4#

If you cross multiply you will get rid of the fractions.

#1 xx(m^2-16) = 6(m-4)" "larr# factorise

#(m+4)(m-4) = 6(m-4)" "larr div (x-4)# on both sides

#m+4 =6#

#m = 2#

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Note that you can also solve the quadratic:

#m^2-16 =6m-24#

#m^2 -6m +8=0#

#(m-2)(m-2=4)=0#

This gives # m=2 or m=4" " #(reject as invalid)

#m=2#