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How do you solve # x^2/(x +3) (-) 5/(x + 3) =0#?

Answer 1

Nathan Axel

# x^2/(x +3) (-) 5/(x + 3) =0#

the denominator is common here:

# (x^2 - 5)/(x + 3) =0#

# (x^2 - 5) =0 . (x+3)#

# (x^2 - 5) = 0#

# x^2 = 5#

#color(red)( x = +sqrt5 or -sqrt5#

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Answer 2

Genesis Allen

To solve the equation x^2/(x + 3) - 5/(x + 3) = 0, we can first combine the fractions by finding a common denominator. In this case, the common denominator is (x + 3).

Next, we can subtract the fractions by subtracting the numerators while keeping the common denominator.

So, the equation becomes (x^2 - 5)/(x + 3) = 0.

To solve for x, we can set the numerator equal to zero, since a fraction is equal to zero only when its numerator is zero.

Therefore, x^2 - 5 = 0.

To solve this quadratic equation, we can factor it or use the quadratic formula.

Factoring: (x - √5)(x + √5) = 0.

Setting each factor equal to zero, we have x - √5 = 0 or x + √5 = 0.

Solving for x, we get x = √5 or x = -√5.

Therefore, the solutions to the equation x^2/(x + 3) - 5/(x + 3) = 0 are x = √5 and x = -√5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.