Answered

5. Simplify the following expression:
[tex]\[
\frac{5x - y}{10xy} - \frac{x - 5y}{10xy}
\][/tex]

6. Simplify the following expression and choose the correct answer:

[tex]\[
\frac{7x^2 - 36xy + 5y^2}{100x^2 y^2}
\][/tex]

A. [tex]\(\frac{2x + 2y}{5xy}\)[/tex]

B. [tex]\(\frac{5x + 4y}{10xy}\)[/tex]

C. [tex]\(\frac{3x + 2y}{5xy}\)[/tex]

D. [tex]\(\frac{5x + 4y}{10xy}\)[/tex]



Answer :

GinnyAnswer
Sure, let's take a detailed, step-by-step approach to simplify the given expression:

Given:
[tex]\[ \frac{5x - y}{10xy} - \frac{x - 5y}{10xy} \][/tex]

Step 1: Combine the fractions since they have the same denominator.
[tex]\[ \frac{(5x - y) - (x - 5y)}{10xy} \][/tex]

Step 2: Distribute the negative sign in the numerator.
[tex]\[ (5x - y) - (x - 5y) = 5x - y - x + 5y \][/tex]

Step 3: Combine like terms in the numerator.
[tex]\[ 5x - x + 5y - y = 4x + 4y \][/tex]

Step 4: Simplify the expression.
[tex]\[ \frac{4x + 4y}{10xy} \][/tex]

Step 5: Factor out the common factor of 4 from the numerator.
[tex]\[ \frac{4(x + y)}{10xy} \][/tex]

Step 6: Simplify the fraction by dividing both the numerator and the denominator by 2.
[tex]\[ \frac{2(x + y)}{5xy} \][/tex]

Step 7: Break down into two separate fractions.
[tex]\[ \frac{2(x + y)}{5xy} = \frac{2x}{5xy} + \frac{2y}{5xy} \][/tex]

Step 8: Further simplify each separate fraction.
[tex]\[ \frac{2x}{5xy} = \frac{2}{5y} \][/tex]
[tex]\[ \frac{2y}{5xy} = \frac{2}{5x} \][/tex]

Thus, combining these results:
[tex]\[ \frac{2}{5y} + \frac{2}{5x} \][/tex]

Therefore, the simplified expression is:
[tex]\[ \frac{2}{5y} + \frac{2}{5x} \][/tex]

So, the correct answer to part 5 is (B) [tex]\(\frac{2x + 2y}{5xy}\)[/tex].

Other Questions