Simplify (2a)/(a-7)-(4a)/(a^2-14a+49)

Math
2aa-7-4aa2-14a+49
Factor using the perfect square rule.
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Rewrite 49 as 72.
2aa-7-4aa2-14a+72
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅a⋅-7
Simplify.
2ab=-14a
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=a and b=-7.
2aa-7-4a(a-7)2
2aa-7-4a(a-7)2
To write 2aa-7 as a fraction with a common denominator, multiply by a-7a-7.
2aa-7⋅a-7a-7-4a(a-7)2
Write each expression with a common denominator of (a-7)2, by multiplying each by an appropriate factor of 1.
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Multiply 2aa-7 and a-7a-7.
2a(a-7)(a-7)(a-7)-4a(a-7)2
Raise a-7 to the power of 1.
2a(a-7)(a-7)1(a-7)-4a(a-7)2
Raise a-7 to the power of 1.
2a(a-7)(a-7)1(a-7)1-4a(a-7)2
Use the power rule aman=am+n to combine exponents.
2a(a-7)(a-7)1+1-4a(a-7)2
Add 1 and 1.
2a(a-7)(a-7)2-4a(a-7)2
2a(a-7)(a-7)2-4a(a-7)2
Combine the numerators over the common denominator.
2a(a-7)-4a(a-7)2
Simplify the numerator.
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Factor 2a out of 2a(a-7)-4a.
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Factor 2a out of -4a.
2a(a-7)+2a(-2)(a-7)2
Factor 2a out of 2a(a-7)+2a(-2).
2a(a-7-2)(a-7)2
2a(a-7-2)(a-7)2
Subtract 2 from -7.
2a(a-9)(a-7)2
2a(a-9)(a-7)2
Simplify (2a)/(a-7)-(4a)/(a^2-14a+49)

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