How do you combine \frac { 1} { x - 3} + \frac { 1} { ( x - 3) ^ { 2} } - \frac { 1} { ( x - 3) ^ { 3} } into one term?
2 Answers
Explanation:
Take
And, given expression can be written as:
Now solve by equating the denominators:
Substitute values:
Explanation:
"we require the fractions to have a "color(blue)"common denominator"
"the common denominator of "
(x-3),(x-3)^2" and "(x-3)^3" is "(x-3)^3
"multiply numerator/denominator of "
1/(x-3)" by "(x-3)^2
rArr1/(x-3)xx(x-3)^2/(x-3)^2=(x-3)^2/(x-3)^3
"multiply numerator/denominator of"
1/(x-3)^2" by "(x-3)
rArr1/(x-3)^2xx(x-3)/(x-3)=(x-3)/(x-3)^3
"putting this together gives"
(x-3)^2/(x-3)^3+(x-3)/(x-3)^3-1/(x-3)^3
"the fractions have a common denominator so add"
"the numerators leaving the common denominator"
=(x^2-6x+9+x-3-1)/(x-3)^3
=(x^2-5x+5)/(x-3)^3to(x!=3)