x^2+3x-10/x^2-2x-35 divide x-2/4x-28
Factorise the expressions first:
x^2+3x-10=(x+5)(x-2)
x^2-2x-35=(x-7)(x+5)
x-2=x-2
4x-28=4(x-7)
Then, invert the second fraction and multiply instead of division:
(x+5)(x-2)/(x-7)(x+5) * 4(x-7)/(x-2)
Simplify the expression by cancelling out common factors:
4(x+5)/(x-7)
ur answer will most likely be 4
Yes, that's correct! The simplified expression is 4(x+5)/(x-7).
To divide rational expressions, you need to first factor each expression and then cancel out any common factors. Let's break down the given expression into its steps:
Step 1: Factor the numerator and denominator of the dividing fraction:
The numerator of the dividing fraction, x^2 + 3x - 10, can be factored as (x + 5)(x - 2).
The denominator of the dividing fraction, x - 2, doesn't have any factors other than x - 2 itself.
Step 2: Factor the numerator and denominator of the fraction being divided:
The numerator of the fraction being divided, x^2 - 2x - 35, can be factored as (x - 7)(x + 5).
The denominator of the fraction being divided, 4x - 28, can be factored as 4(x - 7).
Step 3: Rewrite the expression as a multiplication:
Now that we have factored each expression, we can rewrite the division as a multiplication by multiplying the numerator by the reciprocal of the denominator:
[(x^2 + 3x - 10) / (x^2 - 2x - 35)] * [(4x - 28) / (x - 2)]
Step 4: Cancel out common factors:
We can cancel out the common factors between the numerator and the denominator:
[(x + 5)(x - 2) / (x - 7)(x + 5)] * [4(x - 7) / (x - 2)]
Step 5: Simplify the expression:
After canceling out the common factors, we are left with:
(x - 2) / (x - 7) * 4
Step 6: Multiply the remaining factors:
Multiplying the remaining factors, we get the simplified answer:
4(x - 2) / (x - 7)
Therefore, the simplified expression of (x^2 + 3x - 10) / (x^2 - 2x - 35) divided by (x - 2) / (4x - 28) is 4(x - 2) / (x - 7).