Question 49006
Solve:
{{{4m/(m-3) + 6/(3-m) = m}}} Rewrite the second term on the left side as: {{{-6/(m-3)}}}
{{{4m/(m-3) - 6/(m-3) = m}}} Add the fractions on the left side. The common denominator is (m-3).
{{{(4m-6)/(m-3) = m}}} Multiply both sides by (m-3).
{{{4m-6 = m(m-3)}}} Simplify this.
{{{4m-6 = m^2-3m}}} Subtract 4m from both sides.
{{{-6 = m^2-7m}}} Add 6 to both sides.
{{{m^2-7n+6 = 0}}} Solve this quadratic equation by factoring.
{{{(m-1)(m-6) = 0}}} Apply the zero product principle.
{{{m-1 = 0}}} and/or {{{m-6 = 0}}}
If {{{m-1 = 0}}} then {{{m = 1}}}
If {{{m-6 = 0}}} them m{{{m = 6}}}

Solutions:
m = 1
m = 6

You can check the solutions by substituting them, one-at-a-time into the original equation.