Question

Consider this rational equation. 1 x 1 x − 2 = 1 4 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.

Answer 1

By using least common denominator, the rational equation can be expressed into a standard form quadratic equation as x^2 - 10x + 8 = 0.

In this question,

The rational equation is,

$\frac{1}{x}+\frac{1}{x-2}=\frac{1}{4}$

The standard form quadratic equation can be expressed as

$ax^{2} +bx+c=0$

The above rational equation can be expressed into a standard form quadratic equation by using least common denominator method as,

⇒ $\frac{1}{x}+\frac{1}{x-2}=\frac{1}{4}$

⇒ $\frac{(x-2)+x}{(x)(x-2)}=\frac{1}{4}$

⇒ $\frac{2x-2}{x^{2} -2x}=\frac{1}{4}$

⇒ $4(2x-2)=x^{2} -2x$

⇒ $8x-8=x^{2} -2x$

⇒ $x^{2} -2x-8x+8=0$

⇒ $x^{2} -10x+8=0$

Hence we can conclude that by using least common denominator, the rational equation can be expressed into a standard form quadratic equation as x^2 - 10x + 8 = 0.

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