Question

lesson 25 review - solving rational equations
②
\\(\frac{2a^2}{a^2 - 25} - \frac{a}{(a + 5)} = \frac{7}{(a - 5)}\\)
\\(\frac{2a^2}{(a + 5)(a - 5)} - \frac{a}{(a + 5)} \frac{(a - 5)}{(a - 5)} = \frac{7}{(a - 5)} \frac{(a + 5)}{(a + 5)}\\)
\\(2a^2 - a(a - 5) = 7(a + 5)\\)
\\(2a^2 - a^2 + 5a = 7a + 35\\)
\\(a^2 + 5a = 7a + 35\\)
\\(\frac{-7a \\ -7a}{a^2 - 2a = 35}\\)
\\(\frac{-35 \\ -35}{a^2 - 2a - 35 = 0}\\)
\\(lcd = (a + 5)(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
guess and check factoring right now.
if you set up the big x (as shown from the bonus edpuzzle few days ago), and try to figure out what two numbers multiply to -35, but when added result in -2, the two numbers will be
-4 and 2
-5 and -7
+7 and -5
-7 and +5

Explanation:

Step1: Analyze each option

For each pair of numbers, check their product and sum.

• Option 1: -4 and 2. Product: $(-4)\times2 = -8

eq -35$. Sum: $-4 + 2 = -2$. But product is wrong.

• Option 2: -5 and -7. Product: $(-5)\times(-7)=35

eq -35$. Sum: $-5 + (-7)= -12
eq -2$. Both wrong.

• Option 3: +7 and -5. Product: $7\times(-5)= -35$. Sum: $7 + (-5)=2

eq -2$. Sum is wrong.

• Option 4: -7 and +5. Product: $(-7)\times5 = -35$. Sum: $-7 + 5 = -2$. Both match.

Answer:

D. -7 and +5