Answer:
x = 6 and x = -6
Step-by-step explanation:
[tex] \frac{3 - {x}^{2} }{8 + {x}^{2} } = - \frac{3}{4} [/tex]
i) simplify the equation using cross multiplication
[tex]4(3 - {x}^{2} ) = - 3(8 + x {}^{2} )[/tex]
ii) distribute 4 into (3 - x²)
[tex](4 \times 3) + (4 \times ( - x {}^{2} )) = - 3(8 + {x}^{2} )[/tex]
[tex]12 - 4x {}^{2} = - 3(8 + {x}^{2} )[/tex]
iii) distribute -3 into (8 + x²)
[tex]12 - 4 {x}^{2} = ( - 3 \times 8) + ( - 3 \times {x}^{2} )[/tex]
[tex]12 - 4 {x}^{2} = - 24 - 3 {x}^{2} [/tex]
iv) move -3x² to the left-hand side and change its sign
[tex]12 - 4x {}^{2} + 3 {x}^{2} = - 24[/tex]
v) move 12 to the right-hand side and change its sign
[tex] - 4 {x}^{2} + 3 {x}^{2} = - 24 - 12[/tex]
vi) collect like terms
[tex] - x {}^{2} = - 24 - 12[/tex]
vii) calculate the difference
[tex] - x {}^{2} = - 36[/tex]
viii) change the signs on both sides of the equation
[tex] {x}^{2} = 36[/tex]
ix) take the square root to the opposite side of the equation and remember to use both negative and positive roots
[tex]x = + - \sqrt[]{36} [/tex]
[tex]x = + - 6[/tex]
x) write the solutions one with a '+' sign and the other with a '-' sign
[tex]x = 6[/tex]
[tex]x = - 6[/tex]
