Subtract. Simplify by removing a factor of 1 when possible.
(10bf)/(b^2-f^2)-(b-f)/b+f)
Thank you for your help
hint
b^2-f^2 = (b-f)(b+f)
So, is the answer (b-f)(b+f)? which I think goes at the bottom as a fraction, and if it does, what is the number that goes on top?
However, I could be wrong, can you please help me understand? Thank you.
(10bf)/(b^2-f^2)-(b-f)/b+f)
=(10bf)/((b+f))(b-f)) - (b-f)/(b+f)
Now multiply second term top and bottom by (b-f) to get a common denominator
(10bf)/((b+f))(b-f)) - (b-f)(b-f)/((b+f)(b-f))
You can take it from here.
To subtract the given expression and simplify by removing a factor of 1 when possible, let's break it down step by step:
Step 1: Factorize the denominator in the first term.
The denominator b^2 - f^2 can be factorized as (b - f)(b + f).
Step 2: Rewrite the expression with common denominators.
Now we need to find the common denominator for both terms, which is (b - f)(b + f).
So, rewrite the expression as:
(10bf)/(b - f)(b + f) - (b - f)/(b + f)
Step 3: Simplify the numerators.
Multiply the numerator of the first term by (b + f) and the numerator of the second term by (b - f):
(10bf)(b + f)/(b - f)(b + f) - (b - f)(b - f)/(b + f)
Step 4: Combine the numerators over the common denominator.
Combine the numerators over the common denominator, which will give us:
(10bf)(b + f) - (b - f)(b - f) / (b - f)(b + f)
Step 5: Simplify the expression.
Expand the multiplication for both terms:
= (10b^2f + 10bf^2) - (b^2 - 2bf + f^2) / (b - f)(b + f)
Step 6: Combine like terms in the numerator.
Combine like terms in the numerator:
= 10b^2f + 10bf^2 - b^2 + 2bf - f^2) / (b - f)(b + f)
Step 7: Simplify further, if possible.
No further simplification is possible since no common factors can be removed.
So, the final simplified expression is:
(10b^2f + 10bf^2 - b^2 + 2bf - f^2) / (b - f)(b + f)