Been stuck on this algebra for hours Help is greatly appreci

Been stuck on this algebra for hours. Help is greatly appreciated. Thank you:)!

4. Question from 7.2: Operations on Rational Expressions Add and Subtract. 7x 7 x 7- 3x 5. Question from 7.3: Complex Fractions Simplify. 49_ 6. Question from 7.3: Complex Fractions Simplify. 1

Solution

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

the least common denominator :x( 3-x)

{ 7(7-3x) -7x*x +2x(7-3x) }/x(7-3x)

{ 49 -21x -7x^2 + 14x -6x^2}/x(7-3x)

{-13x^2 -7x+49}/x(7-3x)

2) ( a - 7) /( 49/a -a )

Denominator : 49/a -a = (49 -a^2)/a = (7-a)(7+a)/a

So,  ( a - 7) /( 49/a -a ) = (a- 7)a/( 7-a)(7+a) =a/(7+a)

3) ( x- 1/x)/ (1 +1/x)

Taking x as lcd in numerator and denominator:

(x^2 -1)/(x+1)

we can write : x^2-1 = (x+1)(x-1)

(x^2 -1)/(x+1) = ( x-1)(x+1)/(x+1) = (x-1)

4) x/8 = (x+1)/5

multiply both sides by : 8*5 =40 to eleminatedenominator on both sides

5x = 8(x+1)

5x = 8x +8

-3x = 8

x= -8/3