Question

the sum of the numerator and denominator of a fraction is three less than twice the denominator.if the numerator and denominator is decreased by 1,the numerator becomes half the denominator.find the fraction​

Answer 1

$●L√€.

ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ɪs 4/7

ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ɪs 4/7sᴛᴇᴘ-ʙʏ-sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:

ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ɪs 4/7sᴛᴇᴘ-ʙʏ-sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:ᴛʜᴇ ɢɪᴠᴇɴ ᴘʀᴏʙʟᴇᴍ ɪs ᴏɴ ʟɪɴᴇᴀʀ ᴇǫᴜᴀᴛɪᴏɴs ᴡɪᴛʜ ᴛᴡᴏ ᴠᴀʀɪᴀʙʟᴇs sᴀʏ x ᴀɴᴅ ʏ.

ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ɪs 4/7sᴛᴇᴘ-ʙʏ-sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:ᴛʜᴇ ɢɪᴠᴇɴ ᴘʀᴏʙʟᴇᴍ ɪs ᴏɴ ʟɪɴᴇᴀʀ ᴇǫᴜᴀᴛɪᴏɴs ᴡɪᴛʜ ᴛᴡᴏ ᴠᴀʀɪᴀʙʟᴇs sᴀʏ x ᴀɴᴅ ʏ.ʟᴇᴛ ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ʀᴇǫᴜɪʀᴇᴅ ʙᴇ x/ʏ.

ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ɪs 4/7sᴛᴇᴘ-ʙʏ-sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:ᴛʜᴇ ɢɪᴠᴇɴ ᴘʀᴏʙʟᴇᴍ ɪs ᴏɴ ʟɪɴᴇᴀʀ ᴇǫᴜᴀᴛɪᴏɴs ᴡɪᴛʜ ᴛᴡᴏ ᴠᴀʀɪᴀʙʟᴇs sᴀʏ x ᴀɴᴅ ʏ.ʟᴇᴛ ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ʀᴇǫᴜɪʀᴇᴅ ʙᴇ x/ʏ.sᴜᴍ ᴏғ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ = x + ʏ

ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ɪs 4/7sᴛᴇᴘ-ʙʏ-sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:ᴛʜᴇ ɢɪᴠᴇɴ ᴘʀᴏʙʟᴇᴍ ɪs ᴏɴ ʟɪɴᴇᴀʀ ᴇǫᴜᴀᴛɪᴏɴs ᴡɪᴛʜ ᴛᴡᴏ ᴠᴀʀɪᴀʙʟᴇs sᴀʏ x ᴀɴᴅ ʏ.ʟᴇᴛ ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ʀᴇǫᴜɪʀᴇᴅ ʙᴇ x/ʏ.sᴜᴍ ᴏғ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ = x + ʏɢɪᴠᴇɴ x + ʏ ɪs 3 ʟᴇss ᴛʜᴀɴ ᴛᴡɪᴄᴇ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ → x + ʏ = 2ʏ - 3

ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ɪs 4/7sᴛᴇᴘ-ʙʏ-sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:ᴛʜᴇ ɢɪᴠᴇɴ ᴘʀᴏʙʟᴇᴍ ɪs ᴏɴ ʟɪɴᴇᴀʀ ᴇǫᴜᴀᴛɪᴏɴs ᴡɪᴛʜ ᴛᴡᴏ ᴠᴀʀɪᴀʙʟᴇs sᴀʏ x ᴀɴᴅ ʏ.ʟᴇᴛ ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ʀᴇǫᴜɪʀᴇᴅ ʙᴇ x/ʏ.sᴜᴍ ᴏғ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ = x + ʏɢɪᴠᴇɴ x + ʏ ɪs 3 ʟᴇss ᴛʜᴀɴ ᴛᴡɪᴄᴇ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ → x + ʏ = 2ʏ - 3x - ʏ +3 = 0 → (1)

ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ɪs 4/7sᴛᴇᴘ-ʙʏ-sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:ᴛʜᴇ ɢɪᴠᴇɴ ᴘʀᴏʙʟᴇᴍ ɪs ᴏɴ ʟɪɴᴇᴀʀ ᴇǫᴜᴀᴛɪᴏɴs ᴡɪᴛʜ ᴛᴡᴏ ᴠᴀʀɪᴀʙʟᴇs sᴀʏ x ᴀɴᴅ ʏ.ʟᴇᴛ ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ʀᴇǫᴜɪʀᴇᴅ ʙᴇ x/ʏ.sᴜᴍ ᴏғ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ = x + ʏɢɪᴠᴇɴ x + ʏ ɪs 3 ʟᴇss ᴛʜᴀɴ ᴛᴡɪᴄᴇ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ → x + ʏ = 2ʏ - 3x - ʏ +3 = 0 → (1)ᴀʟsᴏ, ɪғ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ ᴀʀᴇ ᴅᴇᴄʀᴇᴀsᴇᴅ ʙʏ 1 → (x - 1), (ʏ - 1)

ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ɪs 4/7sᴛᴇᴘ-ʙʏ-sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:ᴛʜᴇ ɢɪᴠᴇɴ ᴘʀᴏʙʟᴇᴍ ɪs ᴏɴ ʟɪɴᴇᴀʀ ᴇǫᴜᴀᴛɪᴏɴs ᴡɪᴛʜ ᴛᴡᴏ ᴠᴀʀɪᴀʙʟᴇs sᴀʏ x ᴀɴᴅ ʏ.ʟᴇᴛ ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ʀᴇǫᴜɪʀᴇᴅ ʙᴇ x/ʏ.sᴜᴍ ᴏғ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ = x + ʏɢɪᴠᴇɴ x + ʏ ɪs 3 ʟᴇss ᴛʜᴀɴ ᴛᴡɪᴄᴇ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ → x + ʏ = 2ʏ - 3x - ʏ +3 = 0 → (1)ᴀʟsᴏ, ɪғ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ ᴀʀᴇ ᴅᴇᴄʀᴇᴀsᴇᴅ ʙʏ 1 → (x - 1), (ʏ - 1)ᴛʜᴇ ɴᴜᴍᴇʀᴀᴛᴏʀ ʙᴇᴄᴏᴍᴇs ʜᴀʟғ ᴏғ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ

ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ɪs 4/7sᴛᴇᴘ-ʙʏ-sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:ᴛʜᴇ ɢɪᴠᴇɴ ᴘʀᴏʙʟᴇᴍ ɪs ᴏɴ ʟɪɴᴇᴀʀ ᴇǫᴜᴀᴛɪᴏɴs ᴡɪᴛʜ ᴛᴡᴏ ᴠᴀʀɪᴀʙʟᴇs sᴀʏ x ᴀɴᴅ ʏ.ʟᴇᴛ ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ʀᴇǫᴜɪʀᴇᴅ ʙᴇ x/ʏ.sᴜᴍ ᴏғ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ = x + ʏɢɪᴠᴇɴ x + ʏ ɪs 3 ʟᴇss ᴛʜᴀɴ ᴛᴡɪᴄᴇ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ → x + ʏ = 2ʏ - 3x - ʏ +3 = 0 → (1)ᴀʟsᴏ, ɪғ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ ᴀʀᴇ ᴅᴇᴄʀᴇᴀsᴇᴅ ʙʏ 1 → (x - 1), (ʏ - 1)ᴛʜᴇ ɴᴜᴍᴇʀᴀᴛᴏʀ ʙᴇᴄᴏᴍᴇs ʜᴀʟғ ᴏғ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ x - 1 = \ғʀᴀᴄt{1}{2} (ʏ - 1)x−1=

{1}{2} (ʏ - 1)x−1= 2

{1}{2} (ʏ - 1)x−1= 21

{1}{2} (ʏ - 1)x−1= 21

{1}{2} (ʏ - 1)x−1= 21 (ʏ−1)

{1}{2} (ʏ - 1)x−1= 21 (ʏ−1)2x - 2 = ʏ – 1

{1}{2} (ʏ - 1)x−1= 21 (ʏ−1)2x - 2 = ʏ – 12x - ʏ =2 -1 =1

{1}{2} (ʏ - 1)x−1= 21 (ʏ−1)2x - 2 = ʏ – 12x - ʏ =2 -1 =12x - ʏ = 1 → (2)

{1}{2} (ʏ - 1)x−1= 21 (ʏ−1)2x - 2 = ʏ – 12x - ʏ =2 -1 =12x - ʏ = 1 → (2)sᴜʙᴛʀᴀᴄᴛɪɴɢ (2) ᴀɴᴅ (1) ɢɪᴠᴇs x - ʏ + 3 - (2x - ʏ - 1) = 0

2) ᴀɴᴅ (1) ɢɪᴠᴇs x - ʏ + 3 - (2x - ʏ - 1) = 0x - ʏ + 3 – 2x + ʏ + 1 = 0

2) ᴀɴᴅ (1) ɢɪᴠᴇs x - ʏ + 3 - (2x - ʏ - 1) = 0x - ʏ + 3 – 2x + ʏ + 1 = 0-x + 4 =0

2) ᴀɴᴅ (1) ɢɪᴠᴇs x - ʏ + 3 - (2x - ʏ - 1) = 0x - ʏ + 3 – 2x + ʏ + 1 = 0-x + 4 =0x = 4

2) ᴀɴᴅ (1) ɢɪᴠᴇs x - ʏ + 3 - (2x - ʏ - 1) = 0x - ʏ + 3 – 2x + ʏ + 1 = 0-x + 4 =0x = 4sᴜʙsᴛɪᴛᴜᴛɪɴɢ x ᴠᴀʟᴜᴇ ɪɴ (1) ɢɪᴠᴇs 4 - ʏ + 3 = 0

2) ᴀɴᴅ (1) ɢɪᴠᴇs x - ʏ + 3 - (2x - ʏ - 1) = 0x - ʏ + 3 – 2x + ʏ + 1 = 0-x + 4 =0x = 4sᴜʙsᴛɪᴛᴜᴛɪɴɢ x ᴠᴀʟᴜᴇ ɪɴ (1) ɢɪᴠᴇs 4 - ʏ + 3 = 0ʏ = 7

2) ᴀɴᴅ (1) ɢɪᴠᴇs x - ʏ + 3 - (2x - ʏ - 1) = 0x - ʏ + 3 – 2x + ʏ + 1 = 0-x + 4 =0x = 4sᴜʙsᴛɪᴛᴜᴛɪɴɢ x ᴠᴀʟᴜᴇ ɪɴ (1) ɢɪᴠᴇs 4 - ʏ + 3 = 0ʏ = 7ᴛʜᴇʀᴇғᴏʀᴇ x = 4 ᴀɴᴅ ʏ = 7;

2) ᴀɴᴅ (1) ɢɪᴠᴇs x - ʏ + 3 - (2x - ʏ - 1) = 0x - ʏ + 3 – 2x + ʏ + 1 = 0-x + 4 =0x = 4sᴜʙsᴛɪᴛᴜᴛɪɴɢ x ᴠᴀʟᴜᴇ ɪɴ (1) ɢɪᴠᴇs 4 - ʏ + 3 = 0ʏ = 7ᴛʜᴇʀᴇғᴏʀᴇ x = 4 ᴀɴᴅ ʏ = 7;ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ʀᴇǫᴜɪʀᴇᴅ ɪs 4/7