Question

Simplify completely quantity 7 x squared plus 11 x minus 6 all over quantity 7 x squared minus 10 x plus 3.

Answer 1

     7x^2 + 11x - 6
--------------------------
    7x^2 - 10x + 3

        (7x - 3)(x + 2)
=  -----------------------
        (7x - 3)(x  - 1)
             
        x + 2
=  --------------
        x  - 1

answer is 

quantity x plus 2 over quantity x minus 1

Answer 2

Answer:

$\frac{(x-\frac{3}{7})(x+2)} {(x+\frac{2}{7})(x-1)}$

Explanation:

We have been given the expression$\frac{7x^2+11x-6}{7x^2-10x+3}$

given two expressions are quadratic

Using the formula to solve the quadratic equation is

$D=b^2-4ac$

Now, to solve the equation for x where

$x=\frac{-b\pm\sqrt{D}} {2a}$

general quadratic equation is $ax^2+bx+c$

Comparing the numerator and denominator with general quadratic expression we will get

a=7,b=11,c=-6 in numerator

And a=7,b= -10,c=3 in denominator

And after substituting the values we will get

D=289 for numerator

and $x=\frac{-11\pm17}{14} \\\\\Rightarrow\frac{3}{7} ,-2$

And D=16 in denominator

and $x=\frac{-(-10)\pm4}{14} \\\\\Rightarrow\frac{-2}{7} ,1$

finally we will get $\frac{(x-\frac{3}{7})(x+2)} {(x+\frac{2}{7})(x-1)}$