simplify the following algebraic fractions of different denominator
3/a 7/b - 6/c?
what is the space between 3/a and 7/b supposed to mean?
Also, I'm not sure what you mean by "simplify" since each fraction has a simple denominator. Do you mean add them up to produce one fraction? If so, then the common denominator is clearly "abc"
r4e
To simplify the algebraic fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and then rewrite each fraction with that common denominator.
Let's simplify the expression step by step:
1. Find the LCM of the denominators (a, b, c). The LCM of a set of numbers is the smallest number that is divisible by each number in the set without leaving a remainder. In this case, the LCM of (a, b, c) is "abc" (the product of the three denominators).
2. Rewrite each fraction with the common denominator "abc":
- For the fraction 3/a, multiply the numerator and denominator by (bc) to get:
(3 * bc) / (a * bc) = 3bc / abc.
- For the fraction 7/b, multiply the numerator and denominator by (ac) to get:
(7 * ac) / (b * ac) = 7ac / abc.
- For the fraction -6/c, multiply the numerator and denominator by (ab) to get:
(-6 * ab) / (c * ab) = -6ab / abc.
3. Combine the fractions by adding or subtracting their numerators:
3bc / abc + 7ac / abc - 6ab / abc
4. Since all the fractions now have the same denominator, you can combine the numerators:
(3bc + 7ac - 6ab) / abc
So, the simplified expression is (3bc + 7ac - 6ab) / abc.