Can someone please help me with these algebraic fraction equations

solve and check:
(x-8)/(x+2) = (x+5)/(x+3)


Solve the equation:
(-5x)/(2x + 12) = (2x)/(4x + 24) + (2x - 1)/(x+6)

First : multiplying yields

(x-8)(x+3) = (x+5)(x+2)
=> x²-5x-24 = x²+7x+10
=> 12x = -34
=> x = -17/6

Second : multiplying by 4(x+6) = 4x+24 yields
-10x = 2x + 8x - 4
=> 20x = 4
=> x = 1/5

Your question : multiplying by 4(x+6) yields

(-5x)4(x+6)/2(x+6) = (2x)4(x+6)/4(x+6) + (2x-1)4(x+6)/(x+6)

or (the factors x+6 are in numerator and denominator and cancel out)

2*(-5x) = 2x + 4(2x-1)

-10x = 2x + 8 x - 4

- 10 x = 10x - 4

- 20x = -4

20x = 4

x = 4/20 = 1/5 !

Finally, someone who wrote a rational expression correctly:

(x - 8)/(x + 2) = (x + 5)/(x + 3) \\ multiply both sides by (x + 2)(x + 3) the LCD

(x + 3)(x – 8) = (x + 5)(x + 2) \\ expand each product

x² ‒ 5x – 24 = x² + 7x + 10 \\ subtract x² + 7x + 10 from both sides

0x² + -12x – 34 = 0 \\ it is only a linear equation

x = -34/12 = -17/6 \\ careful, the solution is negative

Check this result in the original equation, I did!

1 (x-8)/(x+2) = (x+5)/(x+3)
(x+2)(x+5)=(x-8)(x+3)
x^2+5x+2x+10=x^2+3x-8x-24
x^2+7x+10=x^2-5x-24
x^2-x^2+7x+5x+10+24=0
12x+34=0
x=-34/12=-17/6
2 (-5x)/(2x + 12) = (2x)/(4x + 24) + (2x - 1)/(x+6)
-5x/2x+12=2x/4x+24+(2x-1/x+6)
-5x(4x+24+(2‏x-1/x+6)=2x(2x+12)
-20x^2-120x+(-10x+5x/x+6)=4x^2+24x
-20x^2-4x^2-120x-24x+(-10x+5x/x-6)=0
-24x^2-144x+(-10x+5x/x-6)=0
-24x^2(x-6)-144x(x-6)-10x+5x=0
do it from now on it's easy lad!!!

Qu 1
(x - 8)(x + 3) = (x + 5)(x + 2)
x² - 5x - 24 = x² + 7x + 10
-34 = 12x
x = - 17/6

Qu 2
(-5x) / [ 2(x + 6) ] = (x) / [ 2(x + 6) ] + (2x - 1) / (x + 6)
-5x = x + 4x - 2
2 = 10x
x = 1/5