What is the right choice for question 25? http://postimage.org/image/igpwul4nr/

Expert Answers
sciencesolve eNotes educator| Certified Educator

You should find the equivalent form of the expression `((6x+5)(x-4)/(x^2+x-20))((x^2-25)/(36x^2-25)) `

Notice that `x^2-25`  and `36x^2-25 `  represent the differences of squares, hence, you should use the special products such that:

`x^2-25 = (x-5)(x+5)` `36x^2-25 = (6x-5)(6x+5)`

You may write the factored form of the denominator `x^2+x-20`  such that:

`x^2+x-20 = (x-x_1)(x-x_2)`

`x_1, x_2`  represent the roots of quadratic

Using the quadratic formula yields:

`x_(1,2) = (-1+-sqrt(1+80))/2 =gt x_(1,2) = (-1+-sqrt81)/2`

`x_(1,2) = (-1+-9)/2 =gt x_1 = -5 ; x_2 = 4`

`x^2+x-20 = (x-4)(x+5)`

You may rewrite the multiplication of fractions such that:


Reducing like terms yields:


Hence, evaluating the equivalent expression yields `(x-5)/(6x-5)` , thus, you need to select the first answer.