Question

x minus one upon X + 2 + x minus 3 upon X + 4 is equal to 10 upon 3

Answer 1

hope it helps you dear

Answer 2

Answer:

x = $-\frac{5}{2},-11$

Step-by-step explanation:

x minus one upon X + 2 can be represented as $\frac{x-1}{x+2}$

x minus 3 upon X + 4 can be represented as $\frac{x-3}{x+4}$

According to question,

x minus one upon X + 2 + x minus 3 upon X + 4 is equal to 10 upon 3, that is,

$\frac{x-1}{x+2}+\frac{x-3}{x+4}=\frac{10}{3}$

$\frac{(x+4)(x-1)+(x-3)(x+2)}{(x+2)(x+4)}=\frac{10}{3}$

$\frac{(x^{2}+4x-x-4)+(x^{2} -3x+2x-6) }{(x^{2}+2x+4x+8 )}=\frac{10}{3}$

$\frac{(x^{2}+3x-4)+(x^{2} -x-6) }{(x^{2}+6x+8 )}=\frac{10}{3}$

$\frac{x^{2}+3x-4+x^{2} -x-6}{(x^{2}+6x+8 )}=\frac{10}{3}$

$\frac{2x^{2}+2x-10}{(x^{2}+6x+8 )}=\frac{10}{3}$

3 ( 2x² + 2x - 10 ) = 10 ( x² + 6x + 8)

6x² + 6x - 30 = 10x² + 60x + 80 = 0

10x² - 6x² + 60x - 6x + 80 + 30 = 0

4x² + 54x + 110 = 0

Dividing the equation by 2,

2x² + 27x + 55 = 0

2x² + 22x + 5x + 55 = 0

2x ( x + 11 ) + 5 ( x + 11 ) = 0

( 2x + 5 ) + ( x + 11 ) = 0

2x + 5 = 0 , x + 11 = 0

x = $-\frac{5}{2}$ , x = -11

Hence,

Answer is x = $-\frac{5}{2},-11$