Mathematics

Question

Which shows the expression x^2-1/x^2-x in simplest form

2 Answer

  • Answer:

    [tex]\large\boxed{\dfrac{x+1}{x}=1+\dfrac{1}{x}}[/tex]

    Step-by-step explanation:

    [tex]\dfrac{x^2-1}{x^2-x}=(*)\\\\x^2-1=x^2-1^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\=(x-1)(x+1)\\\\x^2-x=(x)(x)-(x)(1)\qquad\text{use the distributive property}\\=x(x-1)\\\\(*)=\dfrac{(x-1)(x+1)}{x(x-1)}\qquad\text{cancel}\ (x-1)\\\\=\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}[/tex]

  • The expression x^2-1 / x^2-x 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)(x-1 )}{x(x-1)}[/tex]

    The numerator is split using the identity :

    [tex]a^{2} -b^{2} =(a+b)(a-b)[/tex]

    It can be further simplified as follows:

    [tex]\frac{x^{2}-1 }{x^{2}-x} = \frac{(x+1)(x-1 )}{x(x-1)}\\= \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^2-1 / x^2-x in its simplest form is 1 + 1/x.

    Learn more about simplifying here: https://brainly.com/question/723406

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