Solve this equation, giving your answers correct to 1 decimal place - OCR - GCSE Maths - Question 20 - 2018 - Paper 1

Next, expand the numerator:

$5(x-3) + 3(x+2) = 5x - 15 + 3x + 6 = 8x - 9$

Now, we rewrite the equation as:

$\frac{8x - 9}{(x+2)(x-3)} = 2$

Multiply both sides by ((x+2)(x-3)) to eliminate the fraction:

$8x - 9 = 2(x+2)(x-3)$

Expanding the right side gives:

$2(x^2 - x - 6) = 2x^2 - 2x - 12$

Now, we can rearrange the equation into standard form:

$2x^2 - 10x + 3 = 0$

We can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where (a = 2, b = -10, c = 3). Calculating the discriminant:

$(-10)^2 - 4(2)(3) = 100 - 24 = 76$

Now substituting into the quadratic formula gives:

$x = \frac{10 \pm \sqrt{76}}{4}$

Evaluating this gives two possible solutions:

$x = \frac{10 + \sqrt{76}}{4} \approx 5.3$ $x = \frac{10 - \sqrt{76}}{4} \approx -0.3$

Thus, the solutions are:

Final Answers:

x = -0.3 or x = 5.3 (both rounded to one decimal place)