Simplifying a equation?

[searsp]

Greetings from a particularly miserable England today, miserable as in the weather not the people. Ok we are a pretty miserable nation too.
I'm stuck on my 15 year old's math homework, any help would be gratefully received before I lose the will to live.

Q. Show that 1/(6x^2+7x-5) divided by 1/(4x^2-1) simplifies to ax+b/cx+d where a,b,c and d are integers.

Many thanks
Pete

 

[Deleted member 4993]

Greetings from a particularly miserable England today, miserable as in the weather not the people. Ok we are a pretty miserable nation too.
I'm stuck on my 15 year old's math homework, any help would be gratefully received before I lose the will to live.

Q. Show that 1/(6x^2+7x-5) divided by 1/(4x^2-1) simplifies to (ax+b)/(cx+d) where a,b,c and d are integers.

Many thanks
Pete

\(\displaystyle \displaystyle{\frac{\frac{1}{6x^2+7x-5}}{\frac{1}{4x^2-1}}}\)

\(\displaystyle = \ \displaystyle{\frac{4x^2-1}{6x^2+7x-5}}\)

Now factorize the numerator and the denominator - and simplify by cancelling the common factors.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

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[stapel]

I'm stuck on my 15 year old's math homework....

Why are you doing his/her homework? :shock:

Q. Show that 1/(6x^2+7x-5) divided by 1/(4x^2-1) simplifies to ax+b/cx+d where a,b,c and d are integers.

As currently posted, you have to simplify to this:

. . . . .\(\displaystyle ax\, +\, \dfrac{b}{cx}\, +\, d\)

Was this what you meant? Or is it maybe supposed to be like the following?

. . . . .\(\displaystyle \dfrac{ax\, +\, b}{cx\, +\, d}\)

When you reply, please include a clear listing of your thoughts and efforts so far, so we can figure out what you're needing to review in order to get un-stuck. Thank you!