Which shows the expression x^21/x^2x in simplest form
Question
2 Answer

1. User Answers gmany
Answer:
[tex]\large\boxed{\dfrac{x+1}{x}=1+\dfrac{1}{x}}[/tex]
Stepbystep explanation:
[tex]\dfrac{x^21}{x^2x}=(*)\\\\x^21=x^21^2\qquad\text{use}\ a^2b^2=(ab)(a+b)\\=(x1)(x+1)\\\\x^2x=(x)(x)(x)(1)\qquad\text{use the distributive property}\\=x(x1)\\\\(*)=\dfrac{(x1)(x+1)}{x(x1)}\qquad\text{cancel}\ (x1)\\\\=\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}[/tex]

2. User Answers vipinkumar69547
The expression x^21 / x^2x in its simplest form is 1 + 1/x.
How to simplify a given expression?
The given expression can be simplified by eliminating the common terms from the denominator and numerator. By doing this, the expression can be simplified.
The given expression is:
[tex]\frac{x^{2}1 }{x^{2}x}[/tex]
It can be simplified as shown below:
[tex]\frac{x^{2}1 }{x^{2}x} = \frac{(x+1)(x1 )}{x(x1)}[/tex]
The numerator is split using the identity :
[tex]a^{2} b^{2} =(a+b)(ab)[/tex]
It can be further simplified as follows:
[tex]\frac{x^{2}1 }{x^{2}x} = \frac{(x+1)(x1 )}{x(x1)}\\= \frac{x+1}{x} \\=\frac{x}{x} +\frac{1}{x} \\= 1+\frac{1}{x}[/tex]
We have simplified the given expression into 1 + 1/x.
Thus, the expression x^21 / x^2x in its simplest form is 1 + 1/x.
Learn more about simplifying here: https://brainly.com/question/723406
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