What is the lcd of 1/x +x/2=11/6

[Rhea Suansing]

What is the lcd of 1/x +x/2=11/6

Pleased help me in Solving Quadratic equations and Rational Algebraic Equations

 

[Deleted member 4993]

What is the lcd of 1/x +x/2=11/6

Pleased help me in Solving Quadratic equations and Rational Algebraic Equations

Are you trying to "solve" for 'x'?

 

[Rhea Suansing]

Are you trying to "solve" for 'x'?

Finding the least common denominator

 

[Deleted member 4993]

What is the lcd of 1/x +x/2=11/6

Pleased help me in Solving Quadratic equations and Rational Algebraic Equations

By "lcd" I assume you mean - Least Common Denominator

What are the "denominators" that you need to consider here to calculate the "Least Common Denominator"

 

[Steven G]

What is the lcd of 1/x +x/2=11/6

Pleased help me in Solving Quadratic equations and Rational Algebraic Equations

In the corner of your paper start to write down the lcd by asking yourself the following questions.
Did you write down x (the first denominator) yet? Of course you did not as you did not write down anything yet. So write down x.
Did you write down a 2 yet? Now you did not. So write down a 2 next to the x.
Did you write down a 6 yet. Since 6 is 3*2 you wrote down part of the 6, you now need to write down the 3.
Now multiply everything you wrote down in the corner and that will be your LCD.

 

[HallsofIvy]

On the left side the denominator of the first fraction is "x" and the denominator of the second fraction is "2". Do they have any factors in common? Since x is a variable so you don't know. You certainly know that "2x" is a "common denominator" and you can't really get least common denominator.

So to get a common denominator multiply numerator and denominator of the first fraction by 2 and multiply numerator and denominator of the second fraction by x to get $\displaystyle \frac{2}{2x}+ \frac{x}{2x}= \frac{2+ x}{2x}= \frac{11}{6}$.

(I am not including the "6" as Jomo does because I was only concerned with adding the fractions on the left side.)

Now, as for solving that, a pretty standard way to solve "fraction= fraction" is to eliminate the fraction by multiplying both fraction by those denominators. That is, multiply both sides by 6x: $\displaystyle \frac{2+ x}{2x}(6x)= \frac{11}{6}(6x)$ so $\displaystyle 3(2+ 2x)= 11x$, $\displaystyle 6+ 6x= 11x$, $\displaystyle 6= 5x$.