Question

a ratio is given in the form 2x+5:6x^2+19x+10, write it in the form 1:n, where n is am expression in terms of x

Answer 1

To write the ratio in the form 1:n, we need to divide both terms by the greatest common factor.

First, factor the second term in the ratio: 6x^2 + 19x + 10 = (2x + 5)(3x + 2)

Therefore, the ratio 2x + 5 : 6x^2 + 19x + 10 can be expressed as:
(2x + 5) : (2x + 5)(3x + 2)

Now divide both terms by (2x + 5):
= 1 : 3x + 2

So, the ratio 2x + 5 : 6x^2 + 19x + 10 can be expressed in the form 1 : 3x + 2.