Question

What is the simplified form of the quantity 4 x squared minus 25 over the quantity 2x minus 5 ?

A 2x − 5, with the restriction x ≠ −five over 2

B 2x + 5, with the restriction x ≠ five over 2

C 2x − 5, with the restriction x ≠ five over 2

D 2x + 5, with the restriction x ≠ −five over 2

Answer 1

B) 2x + 5, with the restriction x ≠ five over 2

Explanation:

The given verbal expression is " 4 x squared minus 25 over the quantity 2x minus 5."

Now let's convert this to algebraic expression, we get

`(4x^2 - 25)/(2x - 5)`

Now let's factorize the numerator.

`4x^2 - 25\\= (2x)^2 - 5^2\\= (2x -5)(2x + 5)\\`

We used the identity (a^2 - b^2) = (a -b)(a+b)

=
`((2x - 5)(2x +5))/(2x - 5)`

Here we have (2x - 5) both in the numerator and in the denominator, we can cancel out.

= (2x + 5) where x ≠ 5/2

So the answer is B) 2x + 5, with the restriction x ≠ five over 2

Answer 2

B. 2x + 5, with the restriction x ≠ five over 2

Explanation:

The given expression is the difference of squares, so factors as ...

the product of the quantity 2x plus 5 and the quantity 2x minus 5 over the quantity 2x minus 5

You will note that the numerator and denominator have a common factor:

the quantity 2x minus 5

Factoring that out gives ...

2x + 5, with the restriction x ≠ five over 2 (x is restricted from being a value that makes the denominator zero.)

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Comment on the form of the answer

Since you have written your math expressions using words instead of symbols, we assume you can read them more easily that way. So, we have provided the explanation in the form you can most easily understand. (Personally, I prefer math symbols. They are more compact and tend to be less ambiguous.)