Answered

Get detailed and accurate responses to your questions with IDNLearn.com. Our Q&A platform offers detailed and trustworthy answers to ensure you have the information you need.

Subtract the following rational expressions.

[tex]\[
\frac{9x^2 + 3}{14x^2 - 9} - \frac{-3x^2 + 11}{14x^2 - 9} = \square
\][/tex]

Sagot :

GinnyAnsweridn
Sure! Let's work through the problem step by step:

We are given two rational expressions:

[tex]\[ \frac{9x^2 + 3}{14x^2 - 9} \][/tex]
and
[tex]\[ \frac{-3x^2 + 11}{14x^2 - 9} \][/tex]

We need to subtract the second expression from the first. Since both denominators are the same, we can directly subtract the numerators:

[tex]\[ \frac{9x^2 + 3}{14x^2 - 9} - \frac{-3x^2 + 11}{14x^2 - 9} = \frac{(9x^2 + 3) - (-3x^2 + 11)}{14x^2 - 9} \][/tex]

Let's simplify the numerator:

[tex]\[ (9x^2 + 3) - (-3x^2 + 11) \][/tex]

Distribute the negative sign in the second part:

[tex]\[ 9x^2 + 3 + 3x^2 - 11 \][/tex]

Combine like terms:

[tex]\[ 9x^2 + 3x^2 + 3 - 11 = 12x^2 - 8 \][/tex]

So, the expression simplifies to:

[tex]\[ \frac{12x^2 - 8}{14x^2 - 9} \][/tex]

We can factor out a common factor from the numerator:

[tex]\[ 12x^2 - 8 = 4(3x^2 - 2) \][/tex]

Thus, we have:

[tex]\[ \frac{4(3x^2 - 2)}{14x^2 - 9} \][/tex]

So, the simplified form of the given subtraction is:

[tex]\[ \boxed{\frac{4(3x^2 - 2)}{14x^2 - 9}} \][/tex]
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.