the reciprocal of the expression 2/x + 3/1
To find the reciprocal of an expression, we need to invert it by swapping the numerator and denominator.
Let's start by rewriting the expression: 2/x + 3/1.
The least common denominator (LCD) of x and 1 is simply x.
Now, let's rewrite the expression using the LCD:
2/x + 3/1 = (2/x) + (3/1) * (x/x)
Next, simplify each term:
= 2/x + (3x/1x)
= 2/x + 3x/x
= (2 + 3x)/x
Now, to find the reciprocal, we invert the expression:
Reciprocal = x/(2 + 3x)
So, the reciprocal of the given expression 2/x + 3/1 is x/(2 + 3x).