branscumjaylee
contestada

Enter the correct answer in the box.
Consider this rational equation.
Use the least common denominator to simplify the rational equation into a standard form quadratic equation.
Replace the values of b and c to create the equation.

Enter the correct answer in the box Consider this rational equation Use the least common denominator to simplify the rational equation into a standard form quad class=

Respuesta :

IjlalHashmi

Answer:

[tex]x^2-10x+8=0[/tex]

Step-by-step explanation:

[tex]\frac{1}{x} +\frac{1}{x-2}=\frac{1}{4} \\\\\frac{x-2+x}{x(x-2)} = \frac{1}{4} \\\\\frac{2x-2}{x(x-2)}=\frac{1}{4} \\\\4(2x-2)=x(x-2)\\8x-8=x^2-2x\\0=x^2-2x-8x+8\\0=x^2-10x+8\\x^2-10x+8=0\\[/tex]

akposevictor

Using the least common denominator in simplifying the rational equation, the result of in standard form is: [tex]\mathbf{x^2 -10x + 8 = 0}[/tex]

What is the Least Common Denominator (LCD)?

  • Least common denominator is the smallest common multiple of the denominators of two or more fractions.
  • It is useful when simplifying, adding, subtracting or comparing fractions.

Given:

[tex]\frac{1}{x} + \frac{1}{x - 2} = \frac{1}{4}[/tex]

The least common denominator of the two fractions on the left side of the equation is x(x - 2).

Thus:

[tex]\frac{1(x - 2) + x(1)}{x(x - 2)} = \frac{1}{4}\\\\\frac{x - 2 + x}{x(x - 2)} = \frac{1}{4}\\\\\frac{2x - 2}{x^2 - 2x)} = \frac{1}{4}[/tex]

  • Cross multiply

[tex]4(2x + 2) = 1(x^2 - 2x)\\\\8x + 8 = x^2 - 2x\\\\[/tex]

  • Rewrite in standard form

[tex]0 = x^2 - 2x - 8x + 8\\\\0 = x^2 -10x + 8\\\\\mathbf{x^2 -10x + 8 = 0}[/tex]

Learn more about least common denominator on:

https://brainly.com/question/542317