I don't know how to solve this homework problem.
1 over x+h - 1 over x
________________________
all over h
Can you help?
Of course! I can help you with that homework problem.
To solve this problem, we can start by simplifying the expression.
Let's first look at the numerator, which is: 1/(x + h) - 1/x.
To combine these terms, we need a common denominator. The common denominator in this case is (x)(x + h).
So, let's rewrite the numerator with the common denominator:
[(1)(x) - (1)(x + h)] / [(x + h)(x)]
Simplifying further, we get:
[x - (x + h)] / [(x + h)(x)]
This simplifies to: (-h) / [(x + h)(x)].
Now, let's focus on the denominator of the original expression, which is: h.
To divide by a fraction, we can multiply by its reciprocal. So, we can rewrite the denominator as: 1/h.
Now, let's rewrite the entire expression using the simplified numerator and denominator:
((-h) / [(x + h)(x)]) / (1/h)
To divide by a fraction, we can multiply by the reciprocal of the denominator. Therefore, we can rewrite the expression as follows:
((-h) / [(x + h)(x)]) * (h/1)
The h in the numerator and the h in the denominator cancel out, leaving us with:
(-1) / [(x + h)(x)]
So, the final simplified expression is: -1 / [(x + h)(x)].
I hope this explanation helps you understand how to solve this problem!