1) Solve (8 / x + 2) = (5 / x + 2) + 3x
for x.
What are the two solutions?

2) Solve for x.
( In parentheses means Under the radical sign) (2/7x+5) -4/7 = 4/7

thank you!!

1). 8/(x + 2) = 5/(x + 2) + 3x

Rewrite the expression with common denominator.

8/(x + 2) = [5 + 3x(x + 2)]/(x + 2).

Multiply each side by (x + 2).

8 = [5 + 3x(x + 2)]

Distribute terms using distributive property:  a( b + c) = ab + ac

8 = 5 + 3x2 + 6x

Subtract 8 from each side.

3x2 + 6x - 3 = 0

Divide each side by 3.

x2 + 2x - 1 = 0

Now solve the equation using the factor method.

quadratic formula x = [-b ± √(b2 - 4ac)] / 2a

Compare equation with standard from ax2 + bx + c = 0 and write the coefficients, a = 1, b = 2 and c = -1

Substitute a = 1, b = 2 and c = -1 in the quadratic formula.

x = [-2 ± √(22 - 4(1)(-1))] / 2(1)

x = [-2 ± √(4 + 4] / 2

x = [-2 ± √(8)] / 2

x = [-2 ± 2√2]/2

Take out common term 2.

x = 2[-1 ± √2 ]/2 = [-1 ± √2 ]

Therefore x = [-1 + √2] or x = [-1 - √2].

+1 vote

2). 2/(7x + 5) - 4/7 = 4/7

2/(7x + 5) = 4/7 + 4/7 = 8/7

2/(7x + 5) = 8/7

Cross multiplication.

2(7) = 8(7x + 5)

Divide each side by 2.

7 = 4(7x + 5)

Distribute terms using distributive property:  a( b + c) = ab + ac

7 = 28x + 20.

Subtract 20 from each side.

28x = -13

Divide each side by 28.

x = -13/28.