Question

How do you evaluate the expression $\dfrac{4-y}{1-x}$ when $x=2$ and $y=3$?

Answer 1

Hint: We are given an expression in $x$and$y$. And we are given two values of it which we have to substitute in the expression. Since this is in fraction, we also need to check whether the denominator is turning to 0 or not. We will calculate the numerator and denominator separately and then combine the whole expression. Also, we will take care of the calculation mistakes while evaluating the expression.

Complete step by step solution:
We have an expression given in terms of fraction, so we first take a look at the denominator. We have $1-x$ in the denominator. So, the expression cannot be calculated at $x=1$ which is fine since we are asked to calculate the expression at$x=2$. So, one by one we calculate the numerator and the denominator. The numerator is $4-y$:
$4-y=4-3=1$
Now, we plug $x=2$ in$1-x$, we have:
$1-x=1-2=-1$
Plugging this into the expression we have:
$\dfrac{4-y}{1-x}=\dfrac{1}{-1}=-1$
So, the expression has been evaluated.

Note:
For any such expression involving the roots or the value in the denominator, we first need to check whether calculating that expression at that point is valid or not. After checking the validity of the expression, we simply plug the values. If you are sure about your calculations, you can directly plug the values without separating the numerator and the denominator. But be sure that you are not making any calculation mistakes. Also, do not mix the values while calculating the expression i.e. do not put $x$ in place of $y$ and $y$ in place of$x$.