Question

lesson 2.5 review - solving rational equations
② (\frac{2a^2}{a^2 - 25} - \frac{a}{(a + 5)} = \frac{7}{(a - 5)})
① factor denominators
② find lcd
③ multiply to create lcd
④ solve using numerator
⑤ check for extraneous solutions!
multiple-choice question
factoring (a^2 - 25) can be thought of as (a^2 + 0a - 25), since literally there is no middle term.
now, think about guess and check method for factoring (a^2 + 0a - 25).
youd have to find two numbers that multiply to -25 but add up to 0.
what two numbers satisfy that criteria?
□ 0 and -5
□ -10 and 10
□ -5 and +5
□ -5 and -5
□ 5 and 5

Explanation:

Step1: Analyze the criteria

We need two numbers that multiply to -25 and add up to 0.

Step2: Check each option

• For 0 and -5: \(0\times(-5) = 0

eq - 25\), so this is wrong.

• For - 10 and 10: \((-10)\times10=-100

eq - 25\), so this is wrong.

• For - 5 and + 5: \((-5)\times5=-25\) and \(-5 + 5=0\), this satisfies the criteria.
• For - 5 and - 5: \((-5)\times(-5) = 25

eq - 25\), so this is wrong.

• For 5 and 5: \(5\times5 = 25

eq - 25\), so this is wrong.

Answer:

-5 and + 5 (the option with -5 and + 5)