Question

help? D:

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

2x – 5, with the restriction x ≠ –five over 2

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

2x – 5, with the restriction x ≠ five over 2

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

Answer 1

This?

\( \dfrac{4x^2 - 25}{2x + 5} \)

Answer 2

Yeah

Answer 3

Do you know how to factor a difference of two squares?

Answer 4

This is how you factor the difference of two squares:

\( a^2 - b^2 = (a + b)(a - b) \)

Answer 5

...

Answer 6

In the numerator, you have \(4x^2 - 25 \)
\(4x^2\) is the square of \(2x\)
\(25\) is the square of \(5\)
Your numerator is the difference of two squares.

Answer 7

That means you can factor the nmumerator as:

\( \dfrac{4x^2 - 25}{2x + 5} = \dfrac{(2x + 5)(2x - 5)}{2x + 5} \)

Answer 8

okay

Answer 9

Now you can divide the numerator and denominator by the common factor of
2x + 5:

\( \ = \dfrac{(2x + 5)(2x - 5)}{2x + 5} \)

\( \ = 2x - 5 \)

Answer 10

The fraction simplifies to only
2x - 5,
but since the expression started with a denominator, you need to include the restrictioon that the denominator contains.

The denominator can't equal zero.
To find what value of x makes the denominator zero, set the original denominator equal to zero and solve for x:

\( 2x + 5 = 0\)

\( 2x = -5\)

\(x = -\dfrac{5}{2} \)

Finally you have the complete answer:

\(2x - 5\), \(x \ne -\dfrac{5}{2}\)