Solve the equation 4-x-3-5-2 x-3 - x -0-3-2 for x-

GIven equation : 4/x 3 = 5/2x+3; x ≠ 0, 3/2 4/x 3= 5/2x+3 ⇒4 3x/x=5/2x+3 ⇒(4 3x)(2x+3)=5x ⇒ 6x^2+8x 9x+12=5x ⇒ 6x^2+6x 12=0 ⇒ x^2+x 2=0 ⇒ x^2 2x x 2=0 ⇒ (x+2) ...

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Standard X

Mathematics

Solving Using Quadratic Formula When D>0

Solve the equ...

Question

Solve the equation $\frac{4}{x} - 3 = \frac{5}{2 x + 3}; x \neq 0, - \frac{3}{2}$ for x.

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Solution

GIven equation :
$\frac{4}{x} - 3 = \frac{5}{2 x + 3}; x \neq 0, - \frac{3}{2}$
$\frac{4}{x} - 3 = \frac{5}{2 x + 3} \Rightarrow \frac{4 - 3 x}{x} = \frac{5}{2 x + 3} \Rightarrow (4 - 3 x) (2 x + 3) = 5 x \Rightarrow - 6 x^{2} + 8 x - 9 x + 12 = 5 x \Rightarrow 6 x^{2} + 6 x - 12 = 0 \Rightarrow x^{2} + x - 2 = 0 \Rightarrow x^{2} - 2 x - x - 2 = 0 \Rightarrow (x + 2) (x - 1) = 0 \Rightarrow (x + 2) = 0 (x - 1) = 0 \Rightarrow x = - 2 o r x = 1$
Thus, the solution of the given equation is -2 or 1.

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Solve the equation 4x−3=52x+3;x≠0,−32 for x.

GIven equation : 4x−3=52x+3;x≠0,−32 4x−3=52x+3⇒4−3xx=52x+3⇒(4−3x)(2x+3)=5x⇒−6x2+8x−9x+12=5x⇒6x2+6x−12=0⇒x2+x−2=0⇒x2−2x−x−2=0⇒(x+2)(x−1)=0⇒(x+2)=0(x−1)=0⇒x=−2 or x=1 Thus, the solution of the given equation is -2 or 1.

Solve the equation $\frac{4}{x} - 3 = \frac{5}{2 x + 3}; x \neq 0, - \frac{3}{2}$ for x.