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If
(5)/(x + 2) = (5 - x)/(x - 2) + 1, then x = _____?


\\
A. 2
B. -8
C. 8
D. -2​

User Padi
by
8.3k points

2 Answers

1 vote
To solve the given equation, we can start by simplifying both sides of the equation.

I hope this helps
If (5)/(x + 2) = (5 - x)/(x - 2) + 1, then x = _____? \\ A. 2 B. -8 C. 8 D. -2​-example-1
User Dala
by
8.0k points
1 vote

Answer:

c. 8

Explanation:


\sf (5)/(x + 2) = (5 - x)/(x - 2) + 1

Taking L.C. M. on the right side.


\sf (5)/(x + 2) = (5 - x +(x-2))/(x - 2)

Simplify like terms on the right-hand side


\sf (5)/(x + 2) = (5 - x +x-2)/(x - 2)


\sf (5)/(x + 2) = (3)/(x - 2)

Now, doing criss-cross multiplication:


\sf 5(x-2)=3(x+2)

Open the parenthesis


\sf 5x - 10 = 3x + 6

Subtracting both sides by 3x


\sf 5x-10-3x = 3x +6 -3x

Simplify like terms


\sf 2x - 10 = 6

Add 10 on both sides:


\sf 2x - 10+10 = 6+10


\sf 2x = 16

Divide both sides by 2:


\sf (2x)/(2)=(16)/(2)


\sf x = 8

Therefore, the answer is c. 8

User KorbenDose
by
7.7k points

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