Question
(2) smplify the Hlgebric fraction \( \frac{a b+a c}{a d+98} \)
Ask by Frazier Romero. in Nigeria
Jan 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form of the algebraic fraction is \( \frac{a(b + c)}{ad + 98} \).
Solution
To simplify the algebraic fraction:
\[
\frac{ab + ac}{ad + 98}
\]
**Step 1: Factor the Numerator**
Notice that both terms in the numerator have a common factor of \( a \):
\[
ab + ac = a(b + c)
\]
**Step 2: Rewrite the Fraction**
Substitute the factored form of the numerator back into the fraction:
\[
\frac{a(b + c)}{ad + 98}
\]
**Step 3: Analyze the Denominator**
The denominator \( ad + 98 \) does not have any common factors that can be factored out (assuming \( a \) and \( d \) are variables without specific values that relate to 98). Therefore, it remains unchanged.
**Final Simplified Form:**
\[
\frac{a(b + c)}{ad + 98}
\]
This is the simplest form of the given algebraic fraction.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To simplify the algebraic fraction \( \frac{ab + ac}{ad + 98} \), you can factor the numerator. Notice that you can factor out \( a \) from the numerator: \[ ab + ac = a(b + c) \] This gives you: \[ \frac{a(b + c)}{ad + 98} \] Now, unless \( a(b + c) \) and \( ad + 98 \) have common factors, this is as simplified as it gets! Just remember, it's great to factor whenever possible, as it makes expressions cleaner and easier to work with. If you're feeling adventurous, consider exploring values for \( a, b, c, d \) to see how the simplified expression behaves in different scenarios!
