(5^2-16w+3)/5w^2+24w-5)*(15w^2-8w+1)/(3w^2+14w-5)
There might have been some typos in your question, so I interpreted it as
((5x^2-16x+3)/(5x^2+24x-5))*((15x^2-8x+1)/(3x^2+14x-5))
We factor each quadratic equation inside the parenthesis, and simplify.
((5x^2-16x+3)/(5x^2+24x-5))*((15x^2-8x+1)/(3x^2+14x-5))
((5x-1)(x-3)/(5x-1)(x+5))*((3x-1)(5x-1)/(3x-1)(x+5))
Terms that will be cancelled: 5x-1 and 3x-1
Thus,
(x-3)(5x-1) / ((x+5)(x+5))
And replace the variable x with w.
Hope this helps~ :3
Yes, it does. Thanks so much
To simplify the given expression, you'll need to combine like terms and perform algebraic operations. Let's break it down step by step.
Step 1: Factorize the denominators.
The expression is:
((5^2 - 16w + 3) / (5w^2 + 24w - 5)) * ((15w^2 -8w + 1) / (3w^2 + 14w - 5))
You can factorize the denominators:
5w^2 + 24w - 5
= (5w - 1)(w + 5)
3w^2 + 14w - 5
= (3w - 1)(w + 5)
Step 2: Cross-cancel any common factors between the numerators and denominators.
Comparing the denominators, we see that they share a common factor (w + 5). So, we can simplify the expression further by canceling it out:
((5^2 - 16w + 3) / (5w^2 + 24w - 5)) * ((15w^2 -8w + 1) / (3w^2 + 14w - 5))
= ((5^2 - 16w + 3) / ((5w - 1)(w + 5))) * ((15w^2 -8w + 1) / ((3w - 1)(w + 5)))
= (5^2 - 16w + 3) / ((5w - 1)(3w - 1))
Step 3: Simplify the numerator.
Now, let's simplify the numerator:
The numerator is 5^2 - 16w + 3, which can be simplified to 25 - 16w + 3.
Therefore, the numerator becomes 28 - 16w.
Step 4: Write the final simplified expression.
The simplified expression will be:
(28 - 16w) / ((5w - 1)(3w - 1))
That's it! The given expression has been simplified as much as possible.