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Express 4x/(x^2-9) - 2/(x+3) as a single fraction in its simplest form.

To satisfy the condition of substracting two fractions with unlike denominators, a common denominator needs to be found. By recognizing x^2 - 9 = (x-3)(x+3), we can rewrite the question as 4x/(x-3)(x+3) - [2...
YC
Answered by Ye C. • Maths tutor
6884 Views

Show that r^2(r + 1)^2 - r^2(r - 1)^2 ≡ 4r^3.

Start with the left hand side (LHS) of the equation. r^2(r + 1)^2 - r^2(r - 1)^2Take the equivalent terms from the separate parts of the LHS outside of set of brackets.r^2[(r + 1)^2 - (r - 1)^2]Expand the in...
AD
Answered by Andrew D. • Maths tutor
7918 Views

Two particles, A and B, are moving directly towards each other on a straight line with speeds of 6 m/s and 8 m/s respectively. The mass of A is 3 kg, and the mass of B is 2 kg. They collide to form a single particle of speed "v" m/s. Find v.

The student should apply their knowledge of conservation of momentum. Also, I would always encourage the student to draw a diagram for all mechanics questions as it helps visualise the problem.total change i...
KH
Answered by Kieran H. • Maths tutor
5005 Views

Show that the line with equation ax + by + c = 0 has gradient -a/b and cuts the y axis at -c/b?

This question involves inspecting the answers that have been provided to us. We have been given a constant gradient, and a point at which the line given by the equation cuts the y axis. This, therefore, mean...
DE
Answered by Dominic E. • Maths tutor
9725 Views

Factorise 6x^2 + 7x - 3=0

In order to solve the equation, we need to find a way to break the '7x' term in the middle that allows factorisation. We also need to consider the fact that the last term '-3x' has a minus sign. This broaden...
SM
Answered by Silvia M. • Maths tutor
8896 Views