Solve rac4r−36r+1 = rac2r−13r+4

Question

ScanSolve AI Tutor · Accepted Answer

Here is the solution for question 3 from the image.

3. Solve $\frac{4r-3}{6r+1} = \frac{2r-1}{3r+4}$

Cross-multiply to eliminate the denominators.
$(4r-3)(3r+4) = (2r-1)(6r+1)$
Expand both sides of the equation.
Left side:
$12r^2 + 16r - 9r - 12 = 12r^2 + 7r - 12$
Right side:
$12r^2 + 2r - 6r - 1 = 12r^2 - 4r - 1$
Set the expanded expressions equal to each other.
$12r^2 + 7r - 12 = 12r^2 - 4r - 1$
Subtract $12r^2$ from both sides.
$7r - 12 = -4r - 1$
Add $4r$ to both sides.
$7r + 4r - 12 = -1$ $11r - 12 = -1$
Add 12 to both sides.
$11r = -1 + 12$ $11r = 11$
Divide by 11.
$r = \frac{11}{11}$ $r = 1$
Check for validity (denominators not equal to zero).
For $r=1$ :
$6r+1 = 6(1)+1 = 7 \neq 0$
$3r+4 = 3(1)+4 = 7 \neq 0$
The solution is valid.

Answer