How do you subtract #\frac { 7x } { 4} - \frac { 3x } { 5}#?

Create a common denominator by multiplying the first fraction by
#5/5# and the second fraction by # 4/4# it is important to remember the fairness doctrine whatever is done to one part must be done to all parts of a term

# (7x)/4 xx 5/5 = (35x)/20 #

# (3x)/5 xx 4/4 = ( 12x)/20#

Now that both terms have the same denominator the terms can be subtracted.

# (35x)/20 - (12x)/20 = (23x)/20#

In order to add or subtract fractions, they must have the same denominator, called the least common denominator (LCD). To find the least common denominator, write the multiples for each denominator. The lowest (least) multiple in common is the LCD.

#4:##4,8,12,16,color(red)20,24#
#5:##5,10,15,color(red)20,25#

The LCD is #20#. Now we need to multiply each fraction by an equivalent fraction that is equal to #1#. For example, #2/2=1#, #8/8=1#.

The first fraction needs to be multiplied by #color(red)(5/5# so that its new denominator will be #20#. The second fraction needs to be multiplied by #color(red)(4/4# so that its new denominator will be #20#.

#(7x)/4xxcolor(red)(5/5)-(3x)/5xxcolor(red)(4/4#

Multiply.

#(35x)/20-(12x)/20#

Place the numerators over the denominator #20#.

#(35x-12x)/20#

Simplify.

#23/20#

#23# is a prime number so the fraction cannot be further reduced.