Can someone pls help me with this maths question. tks?

Question

Simplify the following: Y + 7 / 3y² + 20y – 7

I was wondering how to simplify the denominator. What method can I use. I definitely can't use cross factorization can I?

Thanks to all of you who replied. Have a Merry Christmas and A Happy New Year =D

Answer 1

3y^2+20y-7= 3y^2+21y-y-7

3y^2+20y-7= 3y(y+7)-1(y+7)

3y^2+20y-7= (3y-1)(y+7)

Y + 7 / 3y² + 20y – 7= y+7/(3y-1)(y+7)= 1/(3y-1)

Answer 2

When asked to simplify, you should always suspect the numerator is a factor of the denominator.

So, we factor the quadratic on the bottom to see:
3y² + 20y – 7 becomes (y + 7)(3y - 1) and sure enough, we can toss out the common factor of y + 7 to get: 1/ (3y-1) as the answer.

Answer 3

(y+7) is a factor of the denominator. If you do long division of 3y^2+20y-7 by (y+7), you get (3y-1) as the result.

Therefore (y+7)/((y+7)(3y-1)) = 1/(3y-1).

Answer 4

factor 3y^2 + 20y - 7 = (3y - 1)(y+7)

so the expression is simplify to 1/(3y-1)

Answer 5

this problem is an rational algebraic expression with the denominator being a factorable quadratic polynomial. thus,
y+7/3y^2+20y-7 can be simplified into
y+7/(3y-1)(y+7), which in turn becomes : 1/3y-1.

Answer 6

since denominator is a quadratic equation
3y^2+20y-7=3y^2+21y-y-7
=3y(y+7)-(y+7)
=(3y-1)(y+7)

hence the final answer will be 1/(3y-1)

Answer 7

The denominator is a regular quadratic, with:
a=3
b=20
c=-7
Using this info, you can use guess+check and reason to factor the denominator.
(dx+e)(fx+g) You need to find d, e, f, and g. You know that:
d*f=3,
e*g=-7
d*g + e*f=20
Since 3 is prime, you know that there is only one possible integer factorization. 3's factors are 3 and 1, so d and f must be 3 and 1.
Since -7 is also prime, e and g must be 7 and 1 (not in order). -7 is also negative, so either the 1 or the 7 needs to be negative.
Then, try all the combos (3x+7)(1x-1), (3x-7)(1x+1), (3x+1)(1x-7), and (3x-1)(1x+7). Out of these possibilities, only one will fit the previous specification: d*g + e*f=20. In this case it turns out to be (3x-1)(1x+7).

Hope that helps!

Answer 8

3y² + 20y – 7=(3y-1)(y+7)

so we can cancel out out the factor (Y+7) top and bottom
and get

1/(3y-1)

Answer 9

we can do in this way:
y+20y+7 / 3y² -7=21y+7 / 3y² -7=7(3y+1 / 3y² -1)
=7/3y²(9y^3+1+ 3y² )=
7/3y²(9y^3+ 3y²+1)

Answer 10

(y+7) (3y-1) = 3y² + 20y – 7

so you can simplify your answer to become 1/(3y-1)
gluck