((2x^(2)-5x-3)/(x^(2)+x-20))((x^(2)+8x+15)/(2x^(2)+9x+4)) simplify
To simplify this expression, we can first factor each of the quadratic expressions:
The numerator, 2x^2 - 5x - 3, can be factored as (2x + 1)(x - 3).
The denominator, x^2 + x - 20, can be factored as (x + 5)(x - 4).
The first part of the expression becomes:
(2x + 1)(x - 3) / (x + 5)(x - 4).
The second part of the expression, x^2 + 8x + 15, can be factored as (x + 3)(x + 5).
The denominator, 2x^2 + 9x + 4, can be factored as (2x + 1)(x + 4).
The expression becomes:
((2x + 1)(x - 3) / (x + 5)(x - 4)) * ((x + 3)(x + 5) / (2x + 1)(x + 4)).
Simplifying further, we can cancel out the common terms in the numerator and denominator:
(x - 3) / (x - 4) * (x + 3) / (x + 4).
This is the simplified expression.
To simplify the given expression:
1. Factor both the numerator and denominator of the first fraction:
Numerator: 2x^2 - 5x - 3
This can be factored as (2x + 1)(x - 3)
Denominator: x^2 + x - 20
This can be factored as (x + 5)(x - 4)
So, the first fraction becomes [(2x + 1)(x - 3)] / [(x + 5)(x - 4)]
2. Factor both the numerator and denominator of the second fraction:
Numerator: x^2 + 8x + 15
This can be factored as (x + 3)(x + 5)
Denominator: 2x^2 + 9x + 4
This can be factored as (2x + 1)(x + 4)
So, the second fraction becomes [(x + 3)(x + 5)] / [(2x + 1)(x + 4)]
3. Now, multiply the two fractions:
[(2x + 1)(x - 3)] / [(x + 5)(x - 4)] * [(x + 3)(x + 5)] / [(2x + 1)(x + 4)]
4. Simplify by canceling out common factors:
The (2x + 1) terms cancel out, as well as the (x + 5) terms.
This leaves us with:
(x - 3) / (x - 4) * (x + 3) / (x + 4)
5. Multiply the numerators together and the denominators together:
(x - 3)(x + 3) / (x - 4)(x + 4)
6. Expand the numerator and denominator:
(x^2 - 9) / (x^2 - 16)
Therefore, the simplified expression is (x^2 - 9) / (x^2 - 16).
To simplify the expression, we can start by factoring the numerators and denominators separately. Let's begin with the first fraction:
Numerator: 2x^2 - 5x - 3
To factor this quadratic polynomial, we need to find two factors that multiply to -6 (2 * -3) and sum to -5. The factors are -6 and +1. Rewriting the expression:
2x^2 - 6x + x - 3
Now we can factor by grouping:
(2x^2 - 6x) + (x - 3)
Taking out the common factors:
2x(x - 3) + 1(x - 3)
Factoring out (x - 3):
(2x + 1)(x - 3)
Moving on to the denominator of the first fraction:
x^2 + x - 20
This quadratic polynomial can be factored as:
(x + 5)(x - 4)
Therefore, the first fraction can be written as:
(2x + 1)(x - 3) / (x + 5)(x - 4)
Now let's simplify the second fraction:
Numerator: x^2 + 8x + 15
This quadratic polynomial can be factored as:
(x + 3)(x + 5)
Denominator: 2x^2 + 9x + 4
This quadratic polynomial can be factored as:
(2x + 1)(x + 4)
Therefore, the second fraction can be written as:
(x + 3)(x + 5) / (2x + 1)(x + 4)
Now we can combine the two fractions:
(2x + 1)(x - 3) / (x + 5)(x - 4) * (x + 3)(x + 5) / (2x + 1)(x + 4)
We can cancel out the common factors in the numerator and denominator:
[(2x + 1)(x - 3)(x + 3)(x + 5)] / [(x + 5)(x - 4)(2x + 1)(x + 4)]
And finally, we are left with the simplified expression:
(x - 3)(x + 3) / (x - 4)(x + 4)
thats wrong
Apologies for the incorrect response. Let's start again.
To simplify the given expression:
1. Factor the numerator and denominator of the first fraction:
Numerator: 2x^2 - 5x - 3
This can be factored as (2x + 1)(x - 3)
Denominator: x^2 + x - 20
This can be factored as (x + 5)(x - 4)
So, the first fraction becomes [(2x + 1)(x - 3)] / [(x + 5)(x - 4)]
2. Factor the numerator and denominator of the second fraction:
Numerator: x^2 + 8x + 15
This can be factored as (x + 3)(x + 5)
Denominator: 2x^2 + 9x + 4
This can be factored as (x + 4)(2x + 1)
So, the second fraction becomes [(x + 3)(x + 5)] / [(2x + 1)(x + 4)]
3. Now, multiply the two fractions:
[(2x + 1)(x - 3)] / [(x + 5)(x - 4)] * [(x + 3)(x + 5)] / [(2x + 1)(x + 4)]
4. Simplify by canceling out common factors:
The (2x + 1) terms cancel out, leaving us with:
(x - 3) / (x + 4) * (x + 3) / (x - 4)
5. Multiply the numerators together and the denominators together:
(x - 3)(x + 3) / (x + 4)(x - 4)
To simplify further, we can expand the numerator and denominator:
(x^2 - 9) / (x^2 - 16)
Therefore, the simplified expression is (x^2 - 9) / (x^2 - 16).