How do you simplify #\frac { 7} { x - 4} + \frac { 5} { x + 3}#?

1 Answer
Jim G.
Sep 1, 2017

#(12x+1)/((x+3)(x+4))#

Explanation:

#"before we can add the fractions we require them to have"#
#"a "color(blue)"common denominator"#

#"to achieve this"#

#"multiply the numerator/denominator of "7/(x-4)" by "#
#(x+3)#

#"multiply the numerator/denominator of "5/(x+3)" by"#
#(x-4)#

#rArr(7(x+3))/((x+3)(x-4))+(5(x-4))/((x+3)(x-4))#

#"we now have a common denominator so add the"#
#"terms on the numerators while leaving the denominator"#

#=(7x+21+5x-20)/((x+3)(x-4))#

#=(12x+1)/((x+3)(x-4))#

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