Simplify [(1)-(1/x+2)] / [(1)- (3/x+4)]
I know I need to find the LMC here, and the answer is (x+4)/(x+2) but I do not know how to get to the answer and how to use the LMC. I need help!
You need to use more parentheses to distiguish (1/x)+ 2 from 1/(x+2), and (3/x)+4 from 3/(x+4)
I will assume you meant 1/(x+2) and 3/(x+4), since some of those terms appear in the answer
[1-1/(x+2)]/[1 - 3/(x+4)]
= [(x+2-1)/(x+2]]/[(x+4-3)/(x+4)]
=[(x+1)/(x+2)]/[(x+1)/(x+4)]
The x+1 terms cancel, leaving you with
(x+4)/(x+2)
To simplify the expression [(1)-(1/x+2)] / [(1)- (3/x+4)], we can follow these steps:
1. Simplify the denominators:
- The denominator [(1)- (3/x+4)] can be simplified by finding a common denominator, which is (x+4). Multiply the numerator and denominator by (x+4) to get rid of the fraction:
[(1)- (3/x+4)] * [(x+4)/(x+4)] = [(x+4) - (3(x+4))/(x+4)] = (x+4 - 3(x+4))/(x+4) = (x+4 - 3x - 12)/(x+4) = (-2x - 8)/(x+4)
2. Simplify the numerators:
- The numerator [(1)-(1/x+2)] can also be simplified by finding a common denominator, which is (x+2). Multiply the numerator and denominator by (x+2) to eliminate the fraction:
[(1)-(1/x+2)] * [(x+2)/(x+2)] = [(x+2) - (1(x+2))/(x+2)] = (x+2 - (x+2))/(x+2) = 0/(x+2) = 0
3. Simplify the whole expression:
With the simplified numerator and denominator, we can now simplify the entire expression:
0 / ([1] - [3/(x+4)]) = 0 / (1 - (-2x - 8)/(x+4)) = 0 / (1 + (2x + 8)/(x+4)) = 0 / ((x+4 + 2x + 8)/(x+4)) = 0 / ((3x + 12)/(x+4))
When dividing by a fraction, we can multiply by the reciprocal of the fraction:
0 * ((x+4)/(3x + 12)) = 0
Therefore, the simplified expression is 0.