How do you add or subtract #5/(4x^2y) – y/(14xz)#?

Question

Eli Assouline · Accepted Answer

We begin by trying to find a common denominator for these two fractions....
1) The two denominators that we are working with are #4x^2y #and #14xz#
2) To find the LCD we must factor out the two numbers
#14xz = 2 *7 *x*z#
#4x^2y=2^2*x^2*y#
3) Then we find the product of each factor with the highest power
#(2^2)(x^2)(7)(y)(z) = 28x^2yz# Then we try to set each denominator to the LCD that we found   #(28x^2yz)/(28x^2yz)# 28x^2yz)/(28x^2yz)
4) # (5)/(4x^2y)*(7z)/(7z) = (35z)/(28x^2yz)#  #y/(14xz) * (2xy)/(2xy) = (2xy^2)/(28x^2yz)# Now since we have a common denominator, we can now simply the equation into one fraction
#(35z-2xy^2)/(28x^2yz) #
That took forever to write out on this,,,

Jace Anderson · Answer

undefined To add or subtract the given expressions, we need to find a common denominator. The common denominator for 4x^2y and 14xz is 28x^2yz.

To add the expressions, we multiply the numerator and denominator of the first fraction by 7z, and the numerator and denominator of the second fraction by 2x. This gives us (35zy)/(28x^2yz) - (2xy)/(28x^2yz).

Combining the numerators, we have (35zy - 2xy)/(28x^2yz).

To subtract the expressions, we follow the same steps as above, but with a negative sign in front of the second fraction. This gives us (35zy + 2xy)/(28x^2yz).

Therefore, the sum is (35zy - 2xy)/(28x^2yz) and the difference is (35zy + 2xy)/(28x^2yz).