How do you solve # 5 /(x^2 + 4x) = 3 / x - 2/(x + 4)#?

Answer 1
We have : #5/(x^2 + 4x) = 3/x - 2/(x + 4)#.

Let's write all the fractions with the same denominator :

#5/(x^2 + 4x) = 3/x - 2/(x + 4)#
#5/(x^2 + 4x) = (3*(x+4))/(x*(x+4)) - (2*x)/((x + 4)*x)#
#5/(x^2 + 4x) = (3*(x+4))/(x^2+4x) - (2*x)/(x^2+4x)#

Now, let's put all the fractions on the left :

#5/(x^2 + 4x) = (3x+12)/(x^2+4x) - (2x)/(x^2+4x)#
#5/(x^2 + 4x) - (3x+12)/(x^2+4x) + (2x)/(x^2+4x) = 0#
#(5-(3x+12)+ (2x))/(x^2+4x) = 0#
#(5-3x-12+2x)/(x^2+4x) = 0#
#(-x-7)/(x^2+4x) = 0#
#-(x+7)/(x^2+4x) = 0#
We can multiply all the equation by #-(x^2+4x)# :
#x+7 = 0#
That equation #= 0# when #x+7 = 0 => x=-7#.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To solve the equation 5/(x^2 + 4x) = 3/x - 2/(x + 4), we can start by finding a common denominator for the fractions on the right side. The common denominator is x(x + 4).

Multiplying both sides of the equation by x(x + 4), we get:

5(x)(x + 4) = 3(x + 4) - 2(x)

Expanding and simplifying the equation:

5x^2 + 20x = 3x + 12 - 2x

Combining like terms:

5x^2 + 20x = x + 12

Moving all terms to one side of the equation:

5x^2 + 20x - x - 12 = 0

Simplifying further:

5x^2 + 19x - 12 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, factoring is the most efficient method.

Factoring the quadratic equation:

(5x - 3)(x + 4) = 0

Setting each factor equal to zero:

5x - 3 = 0 or x + 4 = 0

Solving for x in each equation:

5x = 3 or x = -4

Dividing both sides by 5:

x = 3/5 or x = -4

Therefore, the solutions to the equation 5/(x^2 + 4x) = 3/x - 2/(x + 4) are x = 3/5 and x = -4.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

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.

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7