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Hi,

Im studying the way to use prefer and rather and am still confused.
I am going to write what im learning and would be very grateful if you can check my mistakes and solve my doubts.

prefer:
1 I prefer cooking by myself / To cook by myself . which one ??? i've read that one is for general situations and the other one specific ones, but i sstill don't get it.

2 comparison: I prefer listening to music to watching tv ( I prefer ing to ing ).

would prefer:
1- I would prefer to be on time

2.comparison: how do i have to do it ?
option 1:
i would prefer to eat here rathar than go home.
option 2:
i would prefer eating here to eating home

would prefer ( object )
i would prefer you to help me

would rather;
i would rather be on time

would rather:( object )
i would rather you helped me

many thanks
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1

I prefer cooking by myself.
I prefer to cook by myself .

There is no significant difference. You can use either one.
There are other verbs similar in this respect, such as like and love.

I like helping people.
I like to help people.

I love going to the beach.
I love to go to the beach.

As we say, it's six of one and half a dozen of the other.
Some verbs are followed by the infinitive, some by the gerund, and some take either one.

Here is a good reference: http://en.wiktionary.org/wiki/Appendix:English_catenative_verbs
Comments  
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2. Would+rather

Would rather is interchangeable with would prefer when choosing between two options.
The verbs are followed by an infinitive clause. Would rather takes the bare infinitive, "would prefer" takes a to-infinitive.

I would rather [to] go to the opera than to the play.
I would prefer to go to the opera than to the play.

He would rather [to] study English than Chinese.
He would prefer to study English than Chinese.

Here are more details:

http://esl.about.com/od/grammarstructures/a/Would-Rather.htm

http://speakspeak.com/english-grammar-exercises/intermediate/would-rather-would-prefer-prefer
Thank you. I will look for more details in your link.