Answer: Our simplified form will be
\(\frac{x+7}{3}\)
Step-by-step explanation:
Since we have given that
\(\frac{5x^2+9x-2}{x^2+12x+20}\times \frac{x^2+17x+70}{15x-3}\)
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
\(\frac{5x^2+9x-2}{x^2+12x+20}\times \frac{x^2+17x+70}{15x-3}\\\\=\frac{(5x-1)(x+2)}{(x+10)(x+2)}\times \frac{(x+10)(x+7)}{15x-3}\\\\=\frac{5x-1}{x+10}\times \frac{(x+10)(x+7)}{3(5x-1)}\\\\=\frac{x+7}{3}\)
