197k views
0 votes
What is the simplified form of the following expression

3x²/x-7-2x/x²-5x-14
a. 3x²-2x/x-7
b. 3x²+2x/x-7
c. 3x²-2x/x²-5x-14



1 Answer

6 votes

Final answer:

To simplify the expression, we factor the denominators and find a common denominator. Then, we combine the numerators over the common denominator and simplify the expression.

Step-by-step explanation:

To simplify the expression $rac{3x^2}{x-7} - rac{2x}{x^2-5x-14}$, we first factor the denominators. The denominator of the first fraction is a binomial $x-7$, which cannot be factored further. The denominator of the second fraction is a trinomial $x^2-5x-14$, which can be factored as $(x-7)(x+2)$. We can now write the expression as $rac{3x^2}{x-7} - rac{2x}{(x-7)(x+2)}$.

To add or subtract fractions with different denominators, we need to find a common denominator. In this case, the common denominator is $(x-7)(x+2)$. To get the first fraction to have this denominator, we need to multiply the numerator and denominator by $(x+2)$. To get the second fraction to have this denominator, we need to multiply the numerator and denominator by $(x-7)$. After performing these operations, we get the expression $rac{3x^2(x+2)}{(x-7)(x+2)} - rac{2x(x-7)}{(x-7)(x+2)}$.

Now, we can combine the numerators over the common denominator, which gives us $rac{3x^2(x+2) - 2x(x-7)}{(x-7)(x+2)}$. Expanding the parentheses, we have $rac{3x^3 + 6x^2 - 2x^2 + 14x}{(x-7)(x+2)}$.

Simplifying the numerator further, we get $rac{3x^3 + 4x^2 + 14x}{(x-7)(x+2)}$. This is the simplified form of the expression.

User Boskom
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories