Algebra 4

4 marks · Hard

Solve the equation . Show all your working clearly.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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x = 3

Common mistakes: Incorrect common denominator.; Errors in cross-multiplication algebra.

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Correctly identifies common denominator ((x-2)(x+3)) and sets up the equation.

M2 · 1 mark · Expands out numerators and combines fractions appropriately. (follow-through)

A1 · 1 mark · Forms correct quadratic or linear equation and simplifies applicable terms. (follow-through)

A2 · 1 mark · Finds correct solution(s) and checks for excluded values. (follow-through)

Worked solution

Multiply both sides by (x-2)(x+3):

Expand each term:

But check calculation again (the expansion steps missed a bracket):

Expanding step by step:

So,

Check:

For x = -13: (x-2) = -15, (x+3) = -10, x+1 = -12

Therefore, x = -13 is a correct solution.