How do you simplify #\frac { 3x + 6} { x ^ { 2} - 5x + 4} - \frac { 3} { x - 1}#?

1 Answer
Jim G.
Oct 25, 2017

#18/((x-1)(x-4))#

Explanation:

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

#"factorise the denominator of the fraction on the left"#

#"the factors of + 4 which sum to - 5 are - 1 and - 4"#

#rArr(3x+6)/((x-1)(x-4))-3/(x-1)#

#"multiply the numerator/denominator of "#

#3/(x-1)" by "(x-4)#

#rArr(3x+6)/((x-1)(x-4))-(3(x-4))/((x-1)(x-4))#

#"now we have a common denominator we can subtract "#
#"the numerators leaving the denominator as it is"#

#rArr(3x+6-3x+12)/((x-1)(x-4))#

#=18/((x-1)(x-4))to(x!=1,x!=4)#

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