Questions: 3/(m-4) = m/(m-2)

Solution Steps

To solve the equation \(\frac{3}{m-4}=\frac{m}{m-2}\), we can use cross-multiplication to eliminate the fractions. This will give us a quadratic equation in terms of \(m\). We then solve the quadratic equation using the quadratic formula or by factoring, if possible.

Starting with the equation

\[ \frac{3}{m-4} = \frac{m}{m-2} \]

we cross-multiply to eliminate the fractions:

\[ 3(m - 2) = m(m - 4) \]

Expanding both sides gives:

\[ 3m - 6 = m^2 - 4m \]

Rearranging the equation leads to:

\[ m^2 - 4m - 3m + 6 = 0 \]

which simplifies to:

\[ m^2 - 7m + 6 = 0 \]

Next, we factor the quadratic equation:

\[ (m - 1)(m - 6) = 0 \]

Setting each factor to zero gives the solutions:

\[ m - 1 = 0 \quad \Rightarrow \quad m = 1 \] \[ m - 6 = 0 \quad \Rightarrow \quad m = 6 \]

Final Answer