Question

Simplify completely quantity 5 x squared plus 9 x minus 2 over quantity x squared plus 12 x plus 20 times quantity x squared plus 17 x plus 70 over quantity 15 x minus 3.

Answer 1

quantity x plus 7 over 3 is the answer for this.

Explanation:

Answer 2

Answer: Our simplified form will be

`(x+7)/(3)`

Explanation:

Since we have given that

`(5x^2+9x-2)/(x^2+12x+20)* (x^2+17x+70)/(15x-3)`

we will factorize the quadratic equations with the help of " Split the middle terms " .

`5x^2+9x-2\\\\=5x^2+10x-x-2\\\\=5x(x+2)-1(x+2)\\\\=(5x-1)(x+2)`

similarly,

`x^2+12x+20\\\\=x^2+10x+2x+20\\\\=x(x+10)+2(x+10)\\\\=(x+10)(x+2)`

Similarly,

`x^2+17x+70\\\\=x^2+10x+7x+70\\\\=x(x+10)+7(x+10)\\\\=(x+10)(x+7)`

Now, our factorized form will be

`(5x^2+9x-2)/(x^2+12x+20)* (x^2+17x+70)/(15x-3)\\\\=((5x-1)(x+2))/((x+10)(x+2))* ((x+10)(x+7))/(15x-3)\\\\=(5x-1)/(x+10)* ((x+10)(x+7))/(3(5x-1))\\\\=(x+7)/(3)`