Divide (1/49-1/(x^2))/(1/7+1/x)

Math
149-1×217+1x
Multiply the numerator and denominator of the complex fraction by 49×2.
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Multiply 149-1×217+1x by 49x249x2.
49x249x2⋅149-1×217+1x
Combine.
49×2(149-1×2)49×2(17+1x)
49×2(149-1×2)49×2(17+1x)
Apply the distributive property.
49×2149+49×2(-1×2)49×217+49x21x
Simplify by cancelling.
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Cancel the common factor of 49.
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Factor 49 out of 49×2.
49(x2)149+49×2(-1×2)49×217+49x21x
Cancel the common factor.
49×2149+49×2(-1×2)49×217+49x21x
Rewrite the expression.
x2+49×2(-1×2)49×217+49x21x
x2+49×2(-1×2)49×217+49x21x
Cancel the common factor of x2.
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Move the leading negative in -1×2 into the numerator.
x2+49×2-1x249x217+49x21x
Factor x2 out of 49×2.
x2+x2⋅49-1x249x217+49x21x
Cancel the common factor.
x2+x2⋅49-1x249x217+49x21x
Rewrite the expression.
x2+49⋅-149×217+49x21x
x2+49⋅-149×217+49x21x
Multiply 49 by -1.
x2-4949×217+49x21x
Cancel the common factor of 7.
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Factor 7 out of 49×2.
x2-497(7×2)17+49x21x
Cancel the common factor.
x2-497(7×2)17+49x21x
Rewrite the expression.
x2-497×2+49x21x
x2-497×2+49x21x
Cancel the common factor of x.
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Factor x out of 49×2.
x2-497×2+x(49x)1x
Cancel the common factor.
x2-497×2+x(49x)1x
Rewrite the expression.
x2-497×2+49x
x2-497×2+49x
x2-497×2+49x
Simplify the numerator.
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Rewrite 49 as 72.
x2-727×2+49x
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x and b=7.
(x+7)(x-7)7×2+49x
(x+7)(x-7)7×2+49x
Factor 7x out of 7×2+49x.
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Factor 7x out of 7×2.
(x+7)(x-7)7x(x)+49x
Factor 7x out of 49x.
(x+7)(x-7)7x(x)+7x(7)
Factor 7x out of 7x(x)+7x(7).
(x+7)(x-7)7x(x+7)
(x+7)(x-7)7x(x+7)
Cancel the common factor of x+7.
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Cancel the common factor.
(x+7)(x-7)7x(x+7)
Rewrite the expression.
x-77x
x-77x
Split the fraction x-77x into two fractions.
x7x+-77x
Cancel the common factor of x.
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Cancel the common factor.
x7x+-77x
Rewrite the expression.
17+-77x
17+-77x
Cancel the common factor of -7 and 7.
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Factor 7 out of -7.
17+7⋅-17x
Cancel the common factors.
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Factor 7 out of 7x.
17+7⋅-17(x)
Cancel the common factor.
17+7⋅-17x
Rewrite the expression.
17+-1x
17+-1x
17+-1x
Move the negative in front of the fraction.
17-1x
Divide (1/49-1/(x^2))/(1/7+1/x)

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