Question

Find the least common denominator of each set of rational algebraic expression.

3/x-4 , 1/x^2 , 2/x^2+4x



PLSSSSSSSSSS ANSWERRRR

Answer 1

Answer:

expressions is

1

.

Explanation:

LCD is Least Common Divisor.

(

x

−

4

)

and

(

x

+

2

)

can be thought of as rational expressions with divisor

1

.

(

x

−

4

)

=

x

−

4

1

and

(

x

+

2

)

=

x

+

2

1

Then the only common divisor (scalar or polynomial) they have is

1

.

If you meant to ask what is the LCD of two rational expressions with denominators

(

x

−

4

)

and

(

x

+

2

)

then the answer is:

(

x

−

4

)

(

x

+

2

)

=

x

2

−

2

x

−

8

The LCD in this case is the LCM (Least Common Multiple) of the two divisors.

Answer link

Answer 2

Answer:

The least common denominator of the given set of algebraic expressions is $x^{4} -16x^{2}$.

Step-by-step explanation:

Given expressions are $\frac{3}{x-4} , \frac{1}{x^{2} } , \frac{2}{x^{2} +4x}$.

The denominators of the expressions are $x-4,x^{2} , x^{2} +4x$.

Now factor the denominators $x-4, x.x, x(x+4)$

To find the least common denominator, we factor the denominators and multiply all the distinct factors.

The distinct factors are $x-4,x,x,x+4$.

The least common denominator is $x^{2} (x+4)(x-4)$

$=x^{2} (x^{2} -16)$

$=x^{4}-16x^{2}$.