Simplifying Complex Expressions

[4hannah]

I’m hoping this question is in the right spot?

(if not, I apologize)

Write x/2 - 2x+4/x+1 as a single fraction.

my approach/steps are as follows:
After finding lowest common denominator,
(2)(x+1),

x(x+1) - 2(2x+4)/(2)(x+1)
= x^2 + x - 4x -8/ 2(x+1)
= x^2 -3x -8/2(x+1)
I know I’m missing something; is this the simplest fractional form?

 

[Dr.Peterson]

Write x/2 - 2x+4/x+1 as a single fraction.

my approach/steps are as follows:
After finding lowest common denominator,
(2)(x+1),

x(x+1) - 2(2x+4)/(2)(x+1)
= x^2 + x - 4x -8/ 2(x+1)
= x^2 -3x -8/2(x+1)
I know I’m missing something; is this the simplest fractional form?

It appears that you omitted some parentheses that are needed to make this mean what you meant. I'll add them for you:

Write x/2 - (2x+4)/(x+1) as a single fraction.​

​

my approach/steps are as follows:​

After finding lowest common denominator,​

(2)(x+1),​

​

[x(x+1) - 2(2x+4)]/[(2)(x+1)]​

= [x^2 + x - 4x -8]/[2(x+1)]​

= [x^2 -3x -8]/[2(x+1)]​

Assuming that is what you meant, you are right so far.

To see if you can go further, you check whether the quadratic numerator can be factored; it can't, so you are finished.

Good work.

 

[4hannah]

It appears that you omitted some parentheses that are needed to make this mean what you meant. I'll add them for you:

Write x/2 - (2x+4)/(x+1) as a single fraction.​

​

my approach/steps are as follows:​

After finding lowest common denominator,​

(2)(x+1),​

​

[x(x+1) - 2(2x+4)]/[(2)(x+1)]​

= [x^2 + x - 4x -8]/[2(x+1)]​

= [x^2 -3x -8]/[2(x+1)]​

Assuming that is what you meant, you are right so far.

To see if you can go further, you check whether the quadratic numerator can be factored; it can't, so you are finished.

Good work.

Thank you so much for the reply and your help (yep, parentheses are definitely in order!)

Thank you for confirming my work.

Kind regards

 

[Steven G]

I’m hoping this question is in the right spot?

(if not, I apologize)

Write x/2 - 2x+4/x+1 as a single fraction.

my approach/steps are as follows:
After finding lowest common denominator,
(2)(x+1),

x(x+1) - 2(2x+4)/(2)(x+1)
= x^2 + x - 4x -8/ 2(x+1)
= x^2 -3x -8/2(x+1)
I know I’m missing something; is this the simplest fractional form?

What if the problem really was [math]\dfrac{x}{2} - 2x +\dfrac{4}{x} + 1[/math], don't you see that you would have written x/2 - 2x+4/x+1? Doesn't that trouble you? After all, writing two very different expressions the same way just can't be correct.