Question

How do you simplify $\dfrac{{{x}^{2}}+5x}{2x}$?

Answer 1

Hint: We have to simplify the given expression. We will first deal with the numerator. We will take $x$ common from the numerator and so we will get the numerator as $x(x+5)$. In the denominator, we have $2x$. $x$ from the numerator and denominator is cancelled and hence, we have the simplified form of the given expression.

Complete step by step solution:
According to the given question, we have to simplify the given fraction of polynomials. The expression we have is,
$\dfrac{{{x}^{2}}+5x}{2x}$-----(1)
We can see that the polynomial in the numerator is of the order 2 and the polynomial in the denominator has a degree of 2.
So, we can see that, in the numerator we can take $x$ common and we get the expression as,
$\Rightarrow \dfrac{x(x+5)}{2x}$------(2)
As we see in the equation (2), that, $x$ is present both in the numerator and in the denominator. And so, we can cancel $x$ from the equation (2) and we get the new expression as,
$\Rightarrow \dfrac{x+5}{2}$

Therefore, the simplified form of the given expression is $\dfrac{x+5}{2}$.

Note: The given expression can also be simplified as,
The expression we have,
$\dfrac{{{x}^{2}}+5x}{2x}$----(1)
We will now split the fraction into two separate fraction and we get it as,
$\Rightarrow \dfrac{{{x}^{2}}}{2x}+\dfrac{5x}{2x}$-----(2)
In the term, $\dfrac{{{x}^{2}}}{2x}$, we have $x$ both in the numerator and in the denominator, so we can cancel it and we get,
$\Rightarrow \dfrac{x}{2}+\dfrac{5x}{2x}$
Similarly, in the term $\dfrac{5x}{2x}$, we have $x$ both in the numerator and in the denominator, so we can cancel it and we get,
$\Rightarrow \dfrac{x}{2}+\dfrac{5}{2}$
We can rewrite it as,
$\Rightarrow \dfrac{x+5}{2}$
Therefore, the simplified form of the given expression is $\dfrac{x+5}{2}$.