How do you divide #\frac { 42x ^ { 4} } { 18x ^ { 7} }#?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Pierre D.
Aug 3, 2017

#7/(3x^3)#

Explanation:

First of all, simplify #42/18#

#42/18 = 7/3#

So #(42x^4)/(18x^7)# can also be expressed as #(7x^4)/(3x^7)#

Then, reduce the fraction with the powers by substracting them

#x^7 - x^4 = x^3#

And the question is where do you place the #x^3# ? Well, it is part of the denominator with the #7# because #x^7# was the biggest between #x^4# so it goes to the denominator

The final answer is : #7/(3x^3)#

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