Question

3-x2/8+x2=-3/4 pls help me
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Answer 1

Answer:

x = 6 and x = -6

Step-by-step explanation:

$\frac{3 - {x}^{2} }{8 + {x}^{2} } = - \frac{3}{4}$

i) simplify the equation using cross multiplication

$4(3 - {x}^{2} ) = - 3(8 + x {}^{2} )$

ii) distribute 4 into (3 - x²)

$(4 \times 3) + (4 \times ( - x {}^{2} )) = - 3(8 + {x}^{2} )$

$12 - 4x {}^{2} = - 3(8 + {x}^{2} )$

iii) distribute -3 into (8 + x²)

$12 - 4 {x}^{2} = ( - 3 \times 8) + ( - 3 \times {x}^{2} )$

$12 - 4 {x}^{2} = - 24 - 3 {x}^{2}$

iv) move -3x² to the left-hand side and change its sign

$12 - 4x {}^{2} + 3 {x}^{2} = - 24$

v) move 12 to the right-hand side and change its sign

$- 4 {x}^{2} + 3 {x}^{2} = - 24 - 12$

vi) collect like terms

$- x {}^{2} = - 24 - 12$

vii) calculate the difference

$- x {}^{2} = - 36$

viii) change the signs on both sides of the equation

${x}^{2} = 36$

ix) take the square root to the opposite side of the equation and remember to use both negative and positive roots

$x = + - \sqrt[]{36}$

$x = + - 6$

x) write the solutions one with a '+' sign and the other with a '-' sign

$x = 6$

$x = - 6$