Simplify x/(x + 5) × (x^2 - 25)/(2x) Step by Step

Step by step

The question

Question: simplify x/(x + 5) × (x² − 25)/2x.

xx + 5 × x² − 252x

1 Factor every part

First the top of the second fraction: x² − 25.

= x² − 25

x² − 25 is x² minus 5 squared.

A square minus a square is the plus bracket times the minus bracket.

a² − b² = (a + b)(a − b)

So the top of the second fraction is (x + 5)(x − 5).

= (x + 5)(x − 5)

2 Cross out the same

Careful!

We cross out only a whole bracket, or a whole x, that multiplies everything.

Never one part of a bracket.

Careful: only whole brackets cross out

Now every part is factored.

A bracket on any top and the same bracket on any bottom make 1.

= x~~(x + 5)~~ × ~~(x + 5)~~(x − 5)2x

(x + 5)/(x + 5) is 1.

Cross them out.

x/x is 1.

Cross them out.

3 Multiply what is left

Top times top, bottom times bottom.

What is left is (x − 5)/2.

= x − 52

One more thing: the bottom of the question can't be 0.

So x can't be −5 or 0.

x ≠ −5, 0

4 Check

Let's check with a number: x = 2.

First in the question.

We get −3/2.

Question: 22 + 5 × 2² − 252(2) = 27 × −214

= −32

Now in our answer.

We get −3/2 too.

Answer: 2 − 52 = −32

Both are −3/2.

So (x − 5)/2 is right!

Let's look back.

First: factor every part.

Then: cross out the same.

Then: multiply what is left.

Last: check.

Answer