What is (a+5)/b =(a-5)/b+(b+5)/a ?

The solution to (a+5)/b =(a-5)/b+(b+5)/a is Parabola with (h,k)=(-5/8 ,-5/2),p= 5/2

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(a+5)/b =(a-5)/b+(b+5)/a

\frac{a + 5}{b} = \frac{a - 5}{b} + \frac{b + 5}{a}

(h, k) = (- \frac{5}{8}, - \frac{5}{2}), p = \frac{5}{2}

Solution steps

\frac{a + 5}{b} = \frac{a - 5}{b} + \frac{b + 5}{a}

Rewrite

\frac{a + 5}{b} - \frac{a - 5}{b} - \frac{b + 5}{a} = 0

in the standard form

4 \cdot \frac{5}{2} (a - (- \frac{5}{8})) = (b - (- \frac{5}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{5}{8}, - \frac{5}{2}), p = \frac{5}{2}

x^{2} + 4 y + 8 = 0

y = x^{2} - 3 \frac{1}{2}

3 x^{2} - y = 4

3 x^{2} - y = 6

x^{2} + 4 x - 8 y - 20 = 0

What is (a+5)/b =(a-5)/b+(b+5)/a ?
The solution to (a+5)/b =(a-5)/b+(b+5)/a is Parabola with (h,k)=(-5/8 ,-5/2),p= 5/2