Simplify x/(3x-6)+1/8

Problem

x/(3*x−6)+1/8

Solution

1. Factor the denominator of the first fraction by pulling out the greatest common factor.

x/(3*(x−2))+1/8

2. Identify the least common denominator (LCD) for the two fractions, which is the product of the unique factors.

LCD=24*(x−2)

3. Rewrite each fraction with the common denominator by multiplying the numerator and denominator by the missing factors.

(x⋅8)/(3*(x−2)⋅8)+(1⋅3*(x−2))/(8⋅3*(x−2))

4. Combine the numerators over the common denominator.

(8*x+3*(x−2))/(24*(x−2))

5. Distribute the 3 in the numerator.

(8*x+3*x−6)/(24*(x−2))

6. Combine like terms in the numerator to reach the final simplified form.

(11*x−6)/(24*(x−2))

Final Answer

x/(3*x−6)+1/8=(11*x−6)/(24*(x−2))

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