MATHEMATICS HIGH SCHOOL

Solve the following equation. Remember to check for extraneous solutions 7/(b+3) + 5/(b-3) = (10b-2)/(b²-9).

Answers

Answer 1

Answer:

Answer:

b= 2 is the solution for the given equation.

Step-by-step explanation:

Here, the given expression is:

$(7)/((b+3)) + (5)/((b-3)) = (10b -2)/((b^(2) -9))$

Simplifying Left side, we get

$(7)/((b+3)) + (5)/((b-3))$

= $(7(b-3) + 5(b+3))/((b+3)(b-3))$

Also, by ALGEBARIC IDENTITY: $x^(2) -y^(2) = (x+y)(x-y)$

So, $(b+3)(b-3) = b^(2) -9$

So, LHS becomes $(7(b-3) + 5(b+3))/(b^(2) -9)$

Compare both Left side, Right side we get

$(7(b-3) + 5(b+3))/(b^(2) -9)$ = $(10b -2)/((b^(2) -9))$

or, 7(b-3) + 5(b+3) = 10b -2

⇒ 7b - 21 + 5b + 15 = 10b -2

or, 12b - 10b = 6-2

or, 2b = 4 ⇒ b = 4/2 = 2

⇒ b= 2 is the solution for the given equation.

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Answers

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Answers

Answer:

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Step-by-step explanation:

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