Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Please could you explain this step by step I’m really stuck.

Please Could You Explain This Step By Step Im Really Stuck class=

Sagot :

chetankachana

Answer:

x = -2.5
x = 2

Step-by-step explanation:

Hello!

We can remove the denominators by multiplying everything by it.

Solve:

  • [tex]\frac{5}{x + 3} + \frac4{x + 2} = 2[/tex]
  • [tex]5 + \frac{4(x + 3)}{x + 2} = 2(x + 3)[/tex]
  • [tex]5 + \frac{4x + 12}{x + 2} = 2x + 6[/tex]
  • [tex]5(x + 2) +4x + 12 = (2x + 6)(x + 2)[/tex]
  • [tex]5x + 10 + 4x + 12 = 2x^2 + 6x + 4x + 12[/tex]
  • [tex]9x + 22 = 2x^2 + 10x + 12[/tex]

Let's make one side equal to 0.

  • [tex]0 = 2x^2 + x - 10[/tex]

Solve by factoring, and then the zero product property.

  • [tex]0 = 2x^2 + x - 10\\[/tex]

Multiply 2 and -10. You get -20. Think of two number that multiply to -20, and add to 1. If we think about the standard form of a quadratic, [tex]ax^2 + bx + c[/tex], think two numbers that equal "ac" and add up to "b".

  • [tex]0 = 2x^2 - 4x + 5x - 10[/tex]
  • [tex]0 = 2x(x - 2) + 5(x - 2)[/tex]
  • [tex]0 = (2x + 5)(x - 2)[/tex]

Using the zero product property, set each factor to 0 and solve for x.

  1. 2x + 5 = 0
    2x = -5
    x = -5/2 = -2.5
  2. x - 2 = 0
    x = 2

The two answers are x = -2.5, and x = 2.

VectorFundament120

Answer:

x = -5/2, 2

Step-by-step explanation:

Given:

[tex]\displaystyle \large{\dfrac{5}{x+3}+\dfrac{4}{x+2} = 2}[/tex]

With restriction that x-values cannot be -3 and -2 else it will turn the expression as in undefined.

First, multiply both sides by (x+3)(x+2) to get rid of the denominator.

[tex]\displaystyle \large{\dfrac{5}{x+3}\cdot (x+2)(x+3)+\dfrac{4}{x+2} \cdot (x+2)(x+3) = 2 \cdot (x+2)(x+3)}\\\\\displaystyle \large{5(x+2)+4(x+3) = 2(x+2)(x+3)}[/tex]

Simplify/Expand in:

[tex]\displaystyle \large{5x+10+4x+12 = 2(x^2+5x+6)}\\\\\displaystyle \large{9x+22=2x^2+10x+12}[/tex]

Arrange the terms or expression in quadratic equation:

[tex]\displaystyle \large{0=2x^2+10x+12-9x-22}\\\\\displaystyle \large{2x^2+x-10=0}[/tex]

Factor the expression:

[tex]\displaystyle \large{(2x+5)(x-2)=0}[/tex]

Solve like linear equation as we get:

[tex]\displaystyle \large{x=-\dfrac{5}{2}, 2}[/tex]

Since both x-values are not exact -2 or -3 - therefore, these values are valid. Hence, x = -5/2, 2

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.