What is the simplified form of this product?((x+1)/(x^2-25))*((x+5)/(x^2+8x+7))
Correct
Well, you know what they say about multiplying fractions - it's like dating a mathematician, it can get complicated. But fear not, I'm here to simplify things for you.
To simplify this product, let's first factorize the denominators:
The denominator of the first fraction, x^2 - 25, can be factored as (x - 5)(x + 5).
The denominator of the second fraction, x^2 + 8x + 7, unfortunately cannot be factored any further.
Now, let's rewrite the product using the factored denominators:
((x + 1)/((x - 5)(x + 5))) * ((x + 5)/(x^2 + 8x + 7))
Next, let's cancel out the common factors in the numerators and denominators:
(x + 1)/(x^2 + 8x + 7)
There you have it! The simplified form of the product is (x + 1)/(x^2 + 8x + 7). Keep in mind that, unfortunately, sometimes there's just no more simplifying we can do - kind of like trying to simplify a clown's outfit, it's already as simple as it gets!
To simplify the given product of fractions, ((x+1)/(x^2-25))*((x+5)/(x^2+8x+7)), we can follow the steps below:
Step 1: Factor the quadratic expressions:
x^2-25 can be factored as (x+5)(x-5)
x^2+8x+7 cannot be factored further.
Step 2: Write the product of the factored expressions:
((x+1)(x+5))/((x+5)(x-5))*((x+5)/(x^2+8x+7))
Step 3: Simplify common factors:
(x+1)/(x-5)*(1/(x^2+8x+7))
Step 4: Rewrite the denominator as a quadratic expression:
(x+1)/(x-5)*(1/[(x+1)(x+7)])
Step 5: Cancel out common terms:
1/(x-5)*(1/(x+7))
Therefore, the simplified form of the given product is 1/(x-5)*(1/(x+7)).
To find the simplified form of the product ((x+1)/(x^2-25))*((x+5)/(x^2+8x+7)), we can follow these steps:
Step 1: Factorize the denominators (x^2-25) and (x^2+8x+7).
(x^2-25) can be factored as (x-5)(x+5).
(x^2+8x+7) cannot be factored further, so we keep it as it is.
Step 2: Simplify the product of the numerators and the denominators.
((x+1)/(x^2-25))*((x+5)/(x^2+8x+7)) = ((x+1)(x+5))/((x-5)(x+5)*(x^2+8x+7))
Step 3: Cancel out any common factors.
In this case, we can cancel out the (x+5) term in the numerator and denominator, as well as the (x-5) term in the denominator. This leaves us with:
((x+1)/(x^2-25))*((x+5)/(x^2+8x+7)) = (x+1)/(x^2+8x+7)
Therefore, the simplified form of the given product is (x+1)/(x^2+8x+7).
1/(x-5)(x+7)
=1/(x^2+2x-35)