Question

x+3/x-1 = 2x+1/3x-5

Solve it quadratic equation

Answer 1

Step-by-step explanation:

Let's solve your equation step-by-step.

x+3x−1=2x+13x−5

x2−x+3x=73x−5

Step 1: Multiply both sides by x.

x2−x+3=73x2−5x

x2−x+3−(73x2−5x)=73x2−5x−(73x2−5x)(Subtract 7/3x^2-5x from both sides)

−43x2+4x+3=0

For this equation: a=-1.3333333333333333, b=4, c=3

−1.333333x2+4x+3=0

x=−b±√b2−4ac2a(Use quadratic formula with a=-1.3333333333333333, b=4, c=3)

x=−(4)±√(4)2−4(−1.333333)(3)2(−1.333333)

x=−4±√32−2.6666666666666665

x=−0.6213203435596427,3.6213203435596424

Check answers. (Plug them in to make sure they work.)

x=−0.62132(Works in original equation)

x=3.62132(Works in original equation)

Answer:

x=−0.62132 or x=3.62132

Answer 2

Step-by-step explanation:

SOLUTION

Given :

$\frac{x + 3}{x - 1} = \frac{2x + 1}{3x - 5}$

$= > (x + 3)(3x - 5) = (x - 1)(2x + 1)$

$= > {3x}^{2} - 5x + 9x - 15 = {2x}^{2} + x - 2x - 1$

$= > {3x}^{2} + 4x - 15 = {2x}^{2} - x - 1$

$= > {3x}^{2} - {2x}^{2} + 4 + x - 15 + 1 = 0$

$= > {x}^{2} + 5x - 14 = 0$

$= > {x}^{2} + 7x - 2x - 14 = 0$

$= > x(x + 7) - 2(x + 7) = 0$

$= > (x + 7)(x - 2) = 0$

$= > x + 7 = 0 \: \: or \: \: x - 2 = 0$

$= > x = - 7 \: \: \: or \: \: \: x = 2.$

Hence :

The roots of the given equation are -7, 2.