How do you simplify #3/(x-3) - 1/x#?

Question

Savannah Anderson · Accepted Answer

#(2x + 3)/(x^2 + 3x)#

First Take The L.C.M of the denominators.

Here L.C.M is #x(x - 3)#.

Now, you have to make the denominators of the expressions same as L.C.M and to do it, you have to multiply both numerators and denominators of the expresions by specific numbers.

So,

#3/(x - 3) - 1/x = (3x)/(x(x - 3)) - (x - 3)/(x(x - 3))#

Now, We can subtract them like we subtract like fractions.

So, #3/(x - 3) - 1/x = (3x)/(x(x - 3)) - (x - 3)/(x(x - 3)) = (3x - (x - 3))/(x(x - 3)) = (3x - x + 3)/(x^2 + 3x) = (2x + 3)/(x^2 + 3x) #

Hence explained.

Hazel Anglin · Answer

undefined To simplify the expression 3/(x-3) - 1/x, we need to find a common denominator and combine the fractions. The common denominator is (x-3)x.

Multiplying the first fraction by x/x and the second fraction by (x-3)/(x-3), we get (3x - 3)/(x(x-3)) - (x-3)/(x(x-3)).

Combining the fractions, we have (3x - 3 - (x-3))/(x(x-3)).

Simplifying further, we get (3x - 3 - x + 3)/(x(x-3)).

This simplifies to (2x)/(x(x-3)).

Therefore, the simplified expression is 2x/(x(x-3)).