Multiply both sides by the Least Common Denominator: \((x-1)(x-4)(x-3)\).
\[(x-4)(x-3)+(x-1)(x-3)=2(x-1)(x-4)\]
Simplify.
\[2{x}^{2}-11x+15=2{x}^{2}-10x+8\]
Cancel \(2{x}^{2}\) on both sides.
\[-11x+15=-10x+8\]
Add \(11x\) to both sides.
\[15=-10x+8+11x\]
Simplify \(-10x+8+11x\) to \(x+8\).
\[15=x+8\]
Subtract \(8\) from both sides.
\[15-8=x\]
Simplify \(15-8\) to \(7\).
\[7=x\]
Switch sides.
\[x=7\]
x=7
