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

Problem

x/(3*x−6)+1/8

Solution

1. Factor the denominator of the first fraction to identify the common components.

x/(3*(x−2))+1/8

2. Find the least common denominator (LCD) by multiplying the unique factors from both denominators.

LCD=24*(x−2)

3. Rewrite each fraction with the LCD 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. Simplify the numerators.

(8*x)/(24*(x−2))+(3*x−6)/(24*(x−2))

5. Combine the fractions by adding the numerators over the common denominator.

(8*x+3*x−6)/(24*(x−2))

6. Combine like terms in the numerator.

(11*x−6)/(24*(x−2))

Final Answer

x/(3*x−6)+1/8=(11*x−6)/(24*x−48)

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