How do you simplify #(a+2b)/(x+a)-(a-2b)/(x-a)-(4bx-2a^2)/(x^2-a^2)#?
2 Answers
Explanation:
Find a common denominator and equivalent fractions:
Explanation:
#"before we can add/subtract fractions we require them to"#
#"have a "color(blue)"common denominator"#
#x^2-a^2" is a "color(blue)"difference of squares"#
#rArra^2-x^2=(x-a)(x+a)#
#"multiply numerator/denominator of "(a+2b)/(x+a)" by "(x-a)#
#"multiply numerator/denominator of "(a-2b)/(x-a)" by "(x+a)#
#((a+2b)(x-a))/((x-a)(x+a))-((a-2b)(x+a))/((x-a)(x+a))-(4bx-2a^2)/((x-a)(x+a))#
#"now add/subtract the numerators leaving the denominator"#
#"first multiplying out the brackets"#
#(ax+2bx-a^2-2ab-(ax-2bx+a^2-2ab)-(4bx-2a^2))/((x-a)(x+a))#
#=(ax+2bx-a^2-2ab-ax+2bx-a^2+2ab-4bx+2a^2)/((x-a)(x+a))#
#=0#