Question

solve for x
negative 1 /x-3 = 2 /x-4
=

Answer 1

To solve the equation

\[
-\frac{1}{x-3} = \frac{2}{x-4},
\]

we can start by cross-multiplying to eliminate the fractions. This gives us:

\[
-1(x - 4) = 2(x - 3).
\]

Expanding both sides yields:

\[
-x + 4 = 2x - 6.
\]

Next, we can rearrange the equation by adding \(x\) to both sides and adding \(6\) to both sides:

\[
4 + 6 = 2x + x,
\]

which simplifies to:

\[
10 = 3x.
\]

Now, we solve for \(x\):

\[
x = \frac{10}{3}.
\]

Thus, the solution is:

\[
x = \frac{10}{3}.
\]

You can verify this solution by substituting \(x = \frac{10}{3}\) back into the original equation.