Andrew M. answered • 12/02/15
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
Basically we are reversing the process where we took
two fractions, found a common denominator, and
combined them.
We have: (2x+3)/(x2+x)
We want the denominator to be two products;
x2+x = x(x+1) so
(2x+3)/(x2+x) = (2x+3)/[x(x+1)]
Our combined fraction was made by multiplying x(x+1) so we
started with fractions that looked like a/x + b/(x+1)
(2x+3)/[x(x+1))] = a/x + b/(x+1)
multiply everything through by x(x+1)
2x+3 = (a/x)[x(x+1)] + [b/(x+1)][x(x+1)]
2x+3 = a(x+1) + b(x)
2x+3 = ax + a + bx
2x+3 = (a+b)x + a
Setting coefficients equal we have:
2 = a+b
a = 3
2 = 3+b
b = -1
Given this our decomposed fractions are
f(x) = 3/x -1/(x+1)
Andrew M.
we have 2x + 3 = (a+b)x + a
Since these expressions are equal then the
coefficient of x on the one side equals the
coefficient of x on the other side so ..
2=a+b
And the exta number on the left will
equal the extra number on the right...
a=3
From those we solve for a and b
and substitute them in the fraction
a/x + b/(x+1)
Hope this helps
Report
12/03/15
Tumaiesla G.
12/02/15