Simplest Form? How to do this?

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1 Answer
Jim G.
Jan 28, 2018

#(x-3)/2#

Explanation:

#"multiply numerator/denominator by x to eliminate"#
#"the fractions"#

#rArr(x-9/x)/(2+6/x)xx x/x#

#=(x^2-9/cancel(x)xxcancel(x))/(2x+6/cancel(x)xxcancel(x))#

#=(x^2-9)/(2x+6)#

#"factorise numerator/denominator"#

#x^2-9" is a "color(blue)"difference of squares"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#"here "a=x" and "b=3#

#rArrx^2-9=(x-3)(x+3)#

#2x+6=2(x+3)larrcolor(blue)"common factor of 2"#

#rArr(x^2-9)/(2x+6)#

#=((x-3)cancel((x+3)))/(2cancel((x+3)))larrcolor(blue)"cancel common factors"#

#=(x-3)/2larr" in form "(A(x+B))/C#

#"with "A=1,B=-3" and "C=2#

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