149-1×217+1x

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

Cancel the common factor of 49.

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.

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.

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.

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

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.

(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.

(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.

x7x+-77x

Rewrite the expression.

17+-77x

17+-77x

Factor 7 out of -7.

17+7⋅-17x

Cancel the common factors.

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)