How do you simplify #\frac { 3} { x + 6} - \frac { 5} { x ^ { 2} - x - 42}#?

1 Answer
Jim G.
Aug 4, 2017

#(3x-26)/((x+6)(x-7))#

Explanation:

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

#"factorising "x^2-x-42#

#"the factors of - 42 which sum to - 1 are - 7 and + 6"#

#rArrx^2-x-42=(x-7)(x+6)#

#rArr3/(x+6)-5/((x+6)(x-7))#

#"multiply the numerator/denominator of " 3/(x+6)#
#"by "(x-7)#

#rArr(3(x-7))/((x+6)(x-7))-5/((x+6)(x-7))#

#"now that the fractions have a common denominator subtract"#
#"the numerators leaving the denominator"#

#(3x-21-5)/((x+6)(x-7))#

#=(3x-26)/((x+6)(x-7))to(x!=-6,7)#

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