How do you combine #1/(2x^2)-5/(2x^2)#?

Question

Eva Abramson · Accepted Answer

Basic principles

Fractions are called rational numbers because they can be expressed in the form of #a/b# Counting numbers are also rational numbers. There form of #a/b# is: #1/1, 2/1, 3/1......# ,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The bottom number is the size indicator of what you are counting. In that #1/2# requires 2 of them to make a whole but there is a count of 1 #2/5# requires 5 of them to make a whole but you have a count of 2 #color(blue)("You can only directly add or subtract the 'counts' if")# #color(blue)("if the size indicators are the same")# #color(brown)("This is why you can directly add "3/1+2/1=5/1)# #color(brown)("People do not write the denominators of 1")# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(green)(1/(2x^2)-5/(2x^2)" have the same size indicator!"# Directly adding the counts give a count of #1+5=6# and the size indicator (DENOMINATOR) is #2x^2# ADDING THE COUNTS DOES NOT CHANGE THE SIZE INDICATOR!

Eva Adamson · Answer

undefined To combine the expressions 1/(2x^2) and -5/(2x^2), you need to find a common denominator. In this case, the common denominator is 2x^2.

To do this, multiply the numerator and denominator of the first fraction, 1/(2x^2), by 5 to get 5/(10x^2).

Now, you can combine the two fractions by subtracting the second fraction, -5/(2x^2), from the first fraction, 5/(10x^2).

Subtracting the fractions gives you (5 - (-5))/(10x^2), which simplifies to 10/(10x^2).

Finally, you can simplify further by canceling out the common factor of 10 in the numerator and denominator, resulting in 1/x^2.