Perform the indicated operations, then simplify.
7x^2/x^2-49 - 7x/x+7+7/x-7
To simplify the expression, first factor the denominators:
x^2 - 49 = (x + 7)(x - 7)
x + 7
x - 7
Now rewrite the expression:
(7x^2 / (x + 7)(x - 7)) - (7x / (x + 7)) + (7 / (x - 7))
Now find a common denominator for the fractions:
[7x^2 - 7x(x - 7) + 7(x + 7)] / (x + 7)(x - 7)
Now simplify the numerator:
[7x^2 - 7x^2 + 49x + 49] / (x + 7)(x - 7)
(49x + 49) / (x + 7)(x - 7)
49(x + 1) / (x + 7)(x - 7)
Therefore, the simplified expression is 49(x + 1) / (x + 7)(x - 7)
maybe the student means (parentheses work wonders)
7x^2/(x^2-49) - 7x/(x+7) + 7/(x-7)
= 7x^2/(x^2-49) - 7x(x-7) / [(x+7)(x-7)] + 7(x+7) / [ (x+7) /(x-7)]
= [ 7x^2 - 7x^2 + 49 x + 7x +49 ] / [ (x+7) /(x-7)]
= (49 x + 7 x + 49) /[ (x+7) /(x-7)]
= [ 56 x + 49] / [ (x+7) /(x-7)]
=7 [ 8x+7] /[ (x+7) /(x-7)]