joshuacezarcla
Answered

Ang Imhr.ca ay narito upang tulungan kang makahanap ng mga sagot sa lahat ng iyong mga katanungan mula sa mga eksperto. Kumuha ng mga sagot mula sa mga eksperto nang mabilis at eksakto mula sa aming dedikadong komunidad ng mga propesyonal. Kumuha ng detalyado at eksaktong sagot sa iyong mga tanong mula sa dedikadong komunidad ng mga eksperto sa aming Q&A platform.

how do you transform a rational algebraic equation into a quadratic equation? explain and give examples.

Sagot :

CebuMath

Answer:

Check the step by step process below.

Step-by-step explanation:

A Rational Equation is an equation composed of rational expressions. A rational expression is in the form of [tex]\frac{f(x)}{q(x)}[/tex] where [tex]q(x)[/tex] is not equal to zero.

A Quadratic Equation is in the form of [tex]ax^2+bx+c=0[/tex] where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are constants but [tex]a\ne0[/tex].

Rational Equation that can be transformed into Quadratic Equation

1. It has to be a rational equation.

2. There should only be one variable.

3. If the expressions are linear, then there should be a variable on both numerator and denominator.

4. If the denominators are all constant, then the numerator should have at least one variable that has a power of 2.

Steps in Transforming a Rational Equation Algebraic Equation into a Quadratic Equation

1. Multiply both sides of the equation by the LCD.

2. Apply the distributive law.

3. Combine like terms.

4. Apply the inverse operation.

5. Rewrite the equation in the form [tex]ax^2+bx+c=0[/tex].

Examples:

In relation to item 3 above. (If the expressions are linear, then there should be a variable on both numerator and denominator. )

             [tex]\begin{aligned}\frac{1+x}{x}+\frac{3x}{x+1}&=-4\\x(x+1)\left(\frac{1+x}{x}+\frac{3x}{x+1}\right)&=x(x+1)(-4)\\\frac{x(x+1)(1+x)}{x}+\frac{x(x+1)(3x)}{x+1}&=-4x^2-4x\\(x+1)(1+x)+x(3x)&=-4x^2-4x\\x^2+2x+1+3x^2&=-4x^2-4x\\4x^2+2x+1&=-4x^2-4x\\4x^2+4x^2+2x+4x+1&=-4x^2+4x^2-4x+4x\\8x^2+6x+1&=0\end{aligned}[/tex]

In relation to item 4 above. ( If the denominators are all constant, then the numerator should have at least one variable that has a power of 2. )

                                   [tex]\begin{aligned}\frac{x^2+1}{3}+\frac{4x+6}{5}&=\frac{6}{7}\\105\left(\frac{x^2+1}{3}+\frac{4x+6}{5}\right)&=105\left(\frac{6}{7}\right)\\\frac{105(x^2+1)}{3}+\frac{105(4x+6)}{5}&=90\\35(x^2+1)+21(4x+6)&=90\\35x^2+35+84x+126&=90\\35x^2+84x+161&=90\\35x^2+84x+161-90&=90-90\\35x^2+84x+71&=0\end{aligned}[/tex]

#LetsStudy

To learn more about rational equations, go to

https://brainly.ph/question/4530840

https://brainly.ph/question/1639804

https://brainly.ph/question/1639804

Umaasa kaming nahanap mo ang hinahanap mo. Huwag mag-atubiling bumalik sa amin para sa higit pang mga sagot at napapanahong impormasyon. Salamat sa pagbisita. Ang aming layunin ay magbigay ng pinaka-tumpak na mga sagot para sa lahat ng iyong pangangailangan sa impormasyon. Bumalik kaagad. Nagagalak kaming sagutin ang iyong mga katanungan dito sa Imhr.ca. Huwag kalimutang bumalik para sa karagdagang kaalaman.