How do you simplify #(36-1/x^2)/(1/(6x^2)-6)#?

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Answer 1 · 2016-10-11T20:49:16

#=-6#

The fractions need to be simplified into one term before you can continue with the division. Find the LCD in each case.

#(36-1/x^2) div (1/(6x^2) -6)#

#= ((36x^2-1)/x^2)div((1-36x^2)/(6x^2))#

Change divide to multiply and invert the fraction.

# =((36x^2-1)/cancel(x^2))xx((6cancel(x^2))/(1-36x^2))#

# =(36x^2-1)xx(-6)/((36x^2-1))" "larr# note the sign switch-round

# =cancel((36x^2-1))xx(-6)/(cancel((36x^2-1))#

#=-6#

Answer 2 · 2016-10-11T20:49:38

#(36-1/(x^2))/(1/(6x^2)-6)=color(green)(-6)#

#36-1/(x^2)#

#color(white)("XXX")=6(6-1/(6x^2))#

#color(white)("XXX")=(-6)(1/(6x^2)-6)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#(36-1/(x^2))/(1/(6x^2)-6)#

#color(white)("XXX")=((-6)(1/(6x^2)-1))/(1/(6x^2)-6)#

#color(white)("XXX")=-6#