Which shows the expressions rewritten with the least common denominator? 7x-2/4x^2 and x-1/8x

Answers

The last one.

\frac{14x - 4}{8x^{2} } and \frac{x^{2} - x}{8x^{2} }

Explanation:

When comparing two fractions with variables like this, it's important to get to the same denominator in order to compare apples with apples and then be able to do not only comparisons but also perform additions/subtractions.

Question is which denominator to use and how to reach it.

In this case, the question and the answer choices do the work for you.  The question asks which one is the LEAST common denominator, and the answers show denominators 8x², 16x² and 16x³.  The smallest of these is 8x².

So, how do we transform each fraction to get to an 8x² denominator? We multiply them by 1, expressed in a different way.  Since we're multiplying by one, we're not affecting the value, just the way it looks.

Let's start with the first one, to get the denominator to go from 4x² to 8x², we need to multiply it by 2... so we'll multiply by 2/2 (which is 1, neutral for the multiplication).

\frac{7x - 2}{4x^{2} }  * \frac{2}{2} = \frac{2(7x - 2)}{2(4x^{2})} = \frac{14x - 4}{8x^{2} }

We do a similar process with the second fraction, but this one to go from 8x to 8x², has to be multiplied by x.

\frac{x - 1}{8x} * \frac{x}{x}  = \frac{x(x - 1)}{x(8x)} = \frac{x^{2} -x}{8x^{2} }

And now you have both fractions on the same denominator, without having changed their value, just their looks

The last one.

\frac{14x - 4}{8x^{2} } and \frac{x^{2} - x}{8x^{2} }

Explanation:

When comparing two fractions with variables like this, it's important to get to the same denominator in order to compare apples with apples and then be able to do not only comparisons but also perform additions/subtractions.

Question is which denominator to use and how to reach it.

In this case, the question and the answer choices do the work for you.  The question asks which one is the LEAST common denominator, and the answers show denominators 8x², 16x² and 16x³.  The smallest of these is 8x².

So, how do we transform each fraction to get to an 8x² denominator? We multiply them by 1, expressed in a different way.  Since we're multiplying by one, we're not affecting the value, just the way it looks.

Let's start with the first one, to get the denominator to go from 4x² to 8x², we need to multiply it by 2... so we'll multiply by 2/2 (which is 1, neutral for the multiplication).

\frac{7x - 2}{4x^{2} }  * \frac{2}{2} = \frac{2(7x - 2)}{2(4x^{2})} = \frac{14x - 4}{8x^{2} }

We do a similar process with the second fraction, but this one to go from 8x to 8x², has to be multiplied by x.

\frac{x - 1}{8x} * \frac{x}{x}  = \frac{x(x - 1)}{x(8x)} = \frac{x^{2} -x}{8x^{2} }

And now you have both fractions on the same denominator, without having changed their value, just their looks

\frac{2p-5}{4p}

Step-by-step explanation:

Least common denominator is the smallest number or expression that can be a common denominator for a set of fractions.

Comparing the two expressions, \frac{2p-5}{4p} and \frac{5p}{6p^{2} },

the common denominator = 24p^{2}, and the highest common factor is 2p.

Therefore, the least common denominator = \frac{24p^{2} }{2p}

                                                                       = 12p

Thus,   \frac{(2p-5)*3}{4p*3}   = \frac{(6p-15)}{12p}

and            \frac{5p*2}{6p^{2}*2 } = \frac{10p}{12p^{2} }

The expression that shows the least common denominator when rewritten is \frac{2p-5}{4p}.

\frac{10x^2+6x}{6x^2} and \frac{21x}{6x^2}.

Step-by-step explanation:

The given expression is:

\frac{5x+3}{3x} and \frac{7x}{3x^2}.

The least common denominator is: 6x^2.

We collect  LCM for the denominator to obtain;

\frac{2x(5x+3)}{6x^2} and \frac{3(7x)}{6x^2}.

We multiply out the parenthesis to obtain;

\frac{10x^2+6x}{6x^2} and \frac{21x}{6x^2}.

Therefore the correct answer is B or the second option.



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