Add (7x+1)/(x^2-36)+(3x)/(x+6)

Math
7x+1×2-36+3xx+6
Simplify the denominator.
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Rewrite 36 as 62.
7x+1×2-62+3xx+6
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x and b=6.
7x+1(x+6)(x-6)+3xx+6
7x+1(x+6)(x-6)+3xx+6
To write 3xx+6 as a fraction with a common denominator, multiply by x-6x-6.
7x+1(x+6)(x-6)+3xx+6⋅x-6x-6
Simplify terms.
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Multiply 3xx+6 and x-6x-6.
7x+1(x+6)(x-6)+3x(x-6)(x+6)(x-6)
Combine the numerators over the common denominator.
7x+1+3x(x-6)(x+6)(x-6)
7x+1+3x(x-6)(x+6)(x-6)
Simplify the numerator.
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Apply the distributive property.
7x+1+3x⋅x+3x⋅-6(x+6)(x-6)
Multiply x by x by adding the exponents.
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Move x.
7x+1+3(x⋅x)+3x⋅-6(x+6)(x-6)
Multiply x by x.
7x+1+3×2+3x⋅-6(x+6)(x-6)
7x+1+3×2+3x⋅-6(x+6)(x-6)
Multiply -6 by 3.
7x+1+3×2-18x(x+6)(x-6)
Subtract 18x from 7x.
-11x+1+3×2(x+6)(x-6)
Reorder terms.
3×2-11x+1(x+6)(x-6)
3×2-11x+1(x+6)(x-6)
Add (7x+1)/(x^2-36)+(3x)/(x+6)

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