Question

Find quadratic equations as follows (a)1/x+a+b = 1/x + 1/a + 1/b . (b) x/3 + 3/x = 17/4. (c) 7x/6 - 30/x = x/3. (d) 3x + 1/3y = 10/3. Plz answer,plz

Answer 1

How can one solve the following by using the method of factorization: 4/x -3 = 5/(2x+3) where x is not equal to 0, -3/2?

[math]\qquad\begin{array}{l} \frac{4}{x}-3=\frac{5}{2x+3}\\ \frac{4-3x}{x}=\frac{5}{2x+3}\\ \left(4-3x\right)\left(2x+3\right)=5x\\ -6x^{2}-x+12=5x\\ -6x^{2}-6x+12=0\\ x^{2}+x-2=0\\ \left(x-1\right)\left(x+2\right)=0\\ x=-2,\;1 \end{array}[/math]