Respuesta :

elcharly64

Answer:

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]

[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]

Step-by-step explanation:

Errors in Algebraic Operations

It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them

  • When we change the signs of all the terms of a polynomial, the expression must be preceded by a negative sign
  • When multiplying negative and positive quantities, if the number of negatives is odd, the result is negative. If the number of negatives is even, the result is positive.
  • Not to confuse product of fractions with the sum of fractions. Rules are quite different

The first expression is

[tex]1-x / (5-x)(-x)=x-1 / x(x-5)[/tex]

Let's arrange into format:

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =\frac{x-1 }{ x(x-5)}[/tex]

We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]

Now for the second expression

[tex]5/s+2/5=2/s[/tex]

Let's arrange into format

[tex]\displaystyle \frac{5}{s}+\frac{2}{5} =\frac{2}{s}[/tex]

It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been

[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]

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