what does x-5 over -3 = 4 over x+3 equal?

Question

what is x+5 = 4

            -3    x+2

Answer 1

I see two problems in the description:

1.) (x-5)/(-3) = 4/(x+3)

2.) (x+5)/(-3) = 4/(x+2)

1.)

(x-5)/(-3) = 4/(x+3)

Can’t divide by zero, so x ≠ -3.

Multiply by -3(x+3)

(x-5)(x+3) = -12

x^2 - 2x - 15 = -12

x^2 - 2x - 3 = 0

(x - 3)(x + 1) = 0

x = -1, 3

Check:

((-1)-5)/(-3) =? 4/((-1)+3)

2 = 2 √

((3)-5)/(-3) =? 4/((3)+3)

2/3 = 2/3 √


2.)

(x+5)/(-3) = 4/(x+2)

Can’t divide by zero, so x ≠ -2.

Multiply be -3(x+2):

(x+5)(x+2) = -12

x^2 + 7x + 10 = -12

x^2 + 7x + 22 = 0

b^2 - 4ac = 49-88 = -39 < 0,
so there will be two complex conjugate roots.

x = (-7 ± i√(39))/2

check:

(((-7 ± i√(39))/2)+10/2)/(-3) =? 4/(((-7 ± i√(39))/2)+4/2)

(-3 ± i√(39))/6 =? 8(3 ± i√(39))/((3 ± i√(39))(-3 ± i√(39)))

(-3 ± i√(39))/6 =? 8(3 ± i√(39))/(-9 - 39)

(-3 ± i√(39))/6 =? 8(3 ± i√(39))/(-48)

(-3 ± i√(39))/6 = (-3 ± i√(39))/6 √

Answer 2

According to my calculations, x=-8/15.

Answer 3

Hi Courtney;

(x+5)/-3=4/(x+2)

Cross-multiply...

(x+5)(x+2)=(-3)(4)

(x+5)(x+2)=-12

Let's FOIL the left side of the equation...

FIRST...(x)(x)=x²

OUTER...(x)(2)=2x

INNER...(5)(x)=5x

LAST...(5)(2)=10

x²+2x+5x+10=-12

x²+7x+10=-12

Let's add 12 to both sides of the equation...

x²+7x+10+12=-12+12

x²+7x+22=0

Quadratic equation...

x=[-b+/-√(b²-4ac)]/2a

b²-4ac=7²-[(4)(1)(22)]=49-88=-39

x=(-7+/-√-39)/[(2)(1)]

x=(-7+/-√-39)/2