Question

perform the operation and combine to one fraction.
\\(\dfrac{3}{x - 4} - \dfrac{7}{x - 6}\\)
answer
attempt 1 out of 2

Explanation:

Step1: Find common denominator

The common denominator of \(x - 4\) and \(x - 6\) is \((x - 4)(x - 6)\).
Rewrite each fraction with the common denominator:
\(\frac{3}{x - 4}=\frac{3(x - 6)}{(x - 4)(x - 6)}\) and \(\frac{7}{x - 6}=\frac{7(x - 4)}{(x - 4)(x - 6)}\)

Step2: Subtract the fractions

\(\frac{3(x - 6)}{(x - 4)(x - 6)}-\frac{7(x - 4)}{(x - 4)(x - 6)}=\frac{3(x - 6)-7(x - 4)}{(x - 4)(x - 6)}\)

Step3: Simplify the numerator

Expand the numerator: \(3x-18 - 7x + 28\)
Combine like terms: \((3x-7x)+(-18 + 28)=-4x + 10\)

Step4: Write the final fraction

The combined fraction is \(\frac{-4x + 10}{(x - 4)(x - 6)}\) (or can be factored as \(\frac{-2(2x - 5)}{(x - 4)(x - 6)}\))

Answer:

\(\frac{-4x + 10}{(x - 4)(x - 6)}\) (or \(\frac{-2(2x - 5)}{(x - 4)(x - 6)}\))